The Blades have been linked with an interest in the England U21 international.
Cresswell has family ties to the club, with his father Richard having made 141 appearances in a United shirt.
The 19-year old is set to have talks with the American coach when the team returns for pre-season training to discuss whether the defender has a place in the first team squad for this campaign.
This could open the door for United to make a move for the exciting young talent if he seeks greater playing time away from Elland Road.
Paul Heckingbottom is hoping to add two defenders to his squad this summer having lost Filip Uremovic and Ben Davies following the conclusion of their loan deals with the club.
Can you remember how much Sheffield United paid for these 22 summer signings?
Cresswell made five Premier League appearances for Leeds last season as the club narrowly avoided relegation to the Championship.
But if the youngster is not guaranteed further playing time over the next 12 months then it is believed he could be offered to Heckingbottom on loan.
If Cresswell wants to compete at international level again then he will need to cement his place in a team at senior level.
Playing first team football in the Championship would be a great opportunity for the defender, who needs that kind of experience to improve.
He could become an important member of Heckingbottom’s side, who will be aiming to push for promotion again over the next year.
Move to Bramall Lane would also be a solid choice logistically as it shouldn’t require a big move away from his current surroundings given the proximity of the two clubs to each other.