The defender is one who the Stamford Bridge club are desperate to sell permanently.
However, there have been no suitors for Chilwell so far this summer, given his injury history.
Per talkSPORT, United could have a chance to bring in Chilwell for a modest fee or even on loan.
Chelsea will not stand in his way, provided the club that takes him pays most of his wages.
"With Chilly it's quite clear," manager Enzo Maresca said in the lead-up to their Premier League opening defeat to Manchester City.
"I love the way he trains, I love the way he is but the problem is that he struggles with us a little bit to find his best position.
"When you train everyday and you don't get minutes, it's not good for them and it's not good for me because I need to make decisions. For some players, it's sometimes better to leave and to go somewhere to get minutes. We will see what happens, the transfer window is open and we will see what happens."