The Premier League ’s return has been exciting and controversial in equal measure.

Two weeks into the new season and there have been shock results, goals aplenty and a healthy dose of VAR-focused furore.

The first few rounds of fixtures have also been revealing, offering an insight into how Liverpool’s title challengers are shaping up for a possible tilt at the Reds’ crown.

While Leicester City and Everton are the surprise early frontrunners, Chelsea, Manchester City and Manchester United have all experienced mixed fortunes so far this term.

All three of City, Chelsea and United have already lost with those defeats highlighting potential flaws in their system.

Jurgen Klopp didn't want Liverpool fans to expect too much too soon of Thiago
Jurgen Klopp and his Liverpool players have enjoyed the dream start to the season with their rivals struggling

Here, with a week remaining until the October 5 transfer deadline, Daily Star Sport looks at where City, Chelsea and United must improve if they are to challenge Liverpool’s supremacy.

Manchester City

After a dominant win over Wolverhampton Wanderers in their season-opener, it looked as though it was going to be business as usual for City as they aim to become top dogs in English football once more.

However, Leicester have forced them into some difficult soul-searching after Sunday’s stunning 5-2 win at the Etihad Stadium.

The Foxes, who have collected maximum points from their opening three games, crushed City thanks to a Jamie Vardy hat-trick, two of which came via the penalty spot, and strikes from James Maddison and Youri Tielemans, the latter of whom also converted from 12 yards.

Jamie Vardy scored three times against Manchester City

While the obvious conclusion would be to highlight City’s defensive frailties, the club have already secured reinforcements in the shape of Benfica’s Ruben Dias, who is set to join for £61m with Nicolas Otamendi heading in the opposite direction.

With Aymeric Laporte close to returning to full fitness after testing positive for coronavirus during pre-season, City will soon have a central defensive partnership much stronger than Eric Garcia and Nathan Ake, who struggled to track Vardy’s runs on Sunday.

The more pressing concern for City chief Pep Guardiola is at the opposite end of the pitch. With Sergio Aguero and Gabriel Jesus both having been ruled out until mid-October at the earliest, City could do with recruiting a striker.

Ruben Dias is close to joining Manchester City
Ruben Dias is close to joining Manchester City

Raheem Sterling struggled to make an impact while leading the line against Leicester before Guardiola turned to 17-year-old debutant Liam Delap as back-up in the second half.

Delap, who scored on his debut against Bournemouth in the Carabao Cup on Thursday, seems a promising prospect, although City need proven match-winners if they are to avoid falling behind Liverpool in the title race once more.

With the Dias deal wrapped up, it will be interesting to see if City target a striker in the final week of the window.

Chelsea

Despite a summer of heavy spending, it has not been plain sailing for Frank Lampard’s new-look Chelsea side.

After beating Brighton & Hove Albion in their opening game, the Blues have stuttered, losing 2-0 to Liverpool before rescuing a 3-3 draw away to West Bromwich Albion, having fallen 3-0 behind at the Hawthorns.

Thiago Silva was at fault for West Brom's second goal
Thiago Silva was at fault for West Brom's second goal, while many other Chelsea team-mates were sloppy against West Brom

Last season, Chelsea’s leaky defence stopped them from keeping pace with Liverpool and City as they conceded 54 goals, more than any other side in the top half of the table.

And while they have signed Thiago Silva and Malang Sarr to beef up Lampard’s backline, they still look shaky at the back.

Goalkeeper Edouard Mendy has joined from Rennes to offer under-fire stopper Kepa Arrizabalaga stiff competition for the No.1 spot in Lampard’s line-up, but central defence remains a problem position with Antonio Rudiger seemingly on his way out.

The Germany international has not been involved in Chelsea’s last three matches having fallen out of favour under Lampard.

Frank Lampard was left frustrated by Chelsea's defence
Frank Lampard was left frustrated by Chelsea's defence at The Hawthorns

Should the 27-year-old depart before the deadline, it seems likely that the Blues will look to secure a replacement.

West Ham United’s Declan Rice has been mentioned frequently as a Chelsea target and the 21-year-old’s ability to play in either midfield or defence does make him a particularly attractive proposition for Lampard.

Timo Werner, Kai Havertz and Hakim Ziyech may combine to transform Chelsea’s attack, but unless they recruit another defensively-minded player, it is difficult to see the Blues sustaining a title challenge this season.

Manchester United

Like City and Chelsea, United’s deficiencies have been laid bare during an up-and-down start to the new Premier League campaign.

Manchester United's Victor Lindelof was surprisingly picked to play against Brighton

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And similar to Chelsea, the Red Devils must address their shortcomings in defence.

Ole Gunnar Solskjaer’s first-choice centre-back pairing of Harry Maguire and Victor Lindelof struggled against Crystal Palace and Brighton, conceding five goals across the two games.

Lindelof, 26, was undone by the pace and power of Palace’s attack at Old Trafford, with Wilfried Zaha, in particular, exposing his lack of conviction during one-on-one situations.

Although Solskjaer has Eric Bailly waiting in the wings, United fans once again called for defensive reinforcements after watching Brighton dominate their side for large spells on Saturday.

Ole Gunnar Solskjaer ended the match as a relieved man
Ole Gunnar Solskjaer ended the Brighton match as a relieved man

There has also been much talk of United’s need for a right-sided attacker. In Anthony Martial, Marcus Rashford and Mason Greenwood, Solskjaer has one of the deadliest attacking trios in the league with that trident having scored a combined 62 goals last season.

However, the gulf in quality from United’s first-choice attackers to the squad players is considerable, with Jesse Lingard, Juan Mata and Daniel James all a long way off their top form.

It remains to be seen if United can convince Borussia Dortmund to part ways with Jadon Sancho, but even if they fail to land the England international, Solskjaer would benefit from the services of another wide man.