Chris Wilder has identified Balogun, 19, as the ideal recruit to bolster his attacking options at Bramall Lane this summer.
The striker, who is yet to make a first-team appearance for Arsenal, has scored 13 goals in 31 games for their Under-23 side.
He was also prolific for the Gunners’ Under-18s, bagging 38 goals in 41 appearances.
But according to the Daily Mail , United have been left stunned by Arsenal’s £15million asking price for Balogun.
Considering he has never made a senior appearance, and has also recently entered the final year of his contract, the Gunners have slapped a surprisingly hefty price tag on their academy star.
He will be free to begin negotiating a move abroad at the turn of the year, which would see Arsenal only receive a small compensation fee next summer.
It is believed a move abroad is becoming more and more likely for him, with United highly unlikely to meet his £15million asking price.
Brentford also failed with a £5million bid for Balogun in the January transfer window.
The New York-born teenager has also earned ten caps for England’s Under-18 outfit, scoring three goals, despite previously representing the United States.
Wilder is on the hunt for attacking reinforcements following United’s 2-0 defeat against Wolves on the opening weekend of the new Premier League season.
Oli McBurnie and Billy Sharp both failed to get on the scoresheet at Bramall Lane, with goals from Raul Jimenez and Romain Saiss sealing the victory for Nuno Espirito Santo’s men.
Get the latest transfer news straight into your inbox!
Want to be on the ball with Jadon Sancho to Manchester United updates? Or perhaps you're a Chelsea fan wondering who on earth could join next?
Well then sign up for the brilliant new Daily Star Sport email newsletter!
From the latest transfer news to the agenda-setting stories, get it all in your email inbox.
How do you sign up?
It only takes a matter of seconds.
Simply type your email address into the box at the top of this article and hit 'subscribe'.
And that's it, job done. You'll receive an email with all of the top news stories every single morning.
You can find out more information on our email newsletter on this link here.
Now the Blades boss wants to strengthen a frontline that also includes David McGoldrick, Lys Mousset and Oliver Burke.
They have also been linked with a move for Liverpool academy graduate Rhian Brewster, who the Premier League champions are ready to cash in on to fund a move for Watford winger Ismaila Sarr.