The Blues accept that in a World Cup year, Pulisic wants regular first-team football.
However, the Daily Mail suggests that owner Todd Boehly will only allow the move under one condition.
If Pulisic wants to play for United on loan this season, he can do so if he agrees to extend his Chelsea contract first.
The 23-year-old has two years to run on his contract, which has Chelsea worried.
Regardless of how he performs this season on loan, he would only have a year left in the summer, which means they cannot sell him for a significant fee.
If he extends his deal by one or two years, Chelsea can protect his value and control his future as well.