The centre-back was a standout player for the La Liga side last season, helping them to Europa League glory and a top four finish.
But, according to Spanish publication Marca, via Sportswitness , Liverpool and United are also ‘in the mix’ to sign him.
Clubs have previously been told that they must meet Carlos' €75m (£68m) release clause if they want to purchase him.
However, the Spanish club are willing to negotiate below that asking price, due to the fact no offers have been submitted yet.
Sevilla want to continue their investment in the squad and could use the money received to bolster the team.
Liverpool were heavily linked with Carlos back in January, with Spanish outlets reporting Jurgen Klopp was ready to break the bank to bring the player in.
The German also reportedly labelled the player as the 'perfect' signing back in April, when Sport reported that the Reds fancied the 27-year-old as Virgil van Dijk's new defensive partner.
City could still come in for the defender, although their top target is Napoli's Kalidou Koulibaly.
Benfica's Ruben Dias and Villarreal's Pau Torres are two other names on Pep Guardiola’s shortlist, despite the club already signing Nathan Ake from Bournemouth this summer.
When quizzed about his future in April, Carlos would not be drawn into any speculation.
“There is a lot of news that comes out and that we see, but I don’t know,” he told Onda Cero.
“What I think is to finish the competition as well as possible and I leave that for later.
“They are very serious things for me and this type of situation must be left for later I am focused exclusively on competition and finishing Sevilla as best as possible.”