Pulisic has emerged as a possible target after United contacted Chelsea to examine whether they would be willing to allow the USMNT international to leave Stamford Bridge.
Pulisic, 23, has two years remaining on his contract. According to sources, he has grown frustrated at his limited game time.
He was a substitute in both Chelsea games so far this season, with appearances totalling 30 minutes. In an injury-hit campaign last term, Pulisic started just 13 Premier League games.
It is unclear whether Chelsea would allow the Pulisic to join a domestic rival, with Newcastle United also thought to be monitoring the situation, although sources have indicated they are more likely to be open to a loan move rather than a permanent transfer.
Sources also suggest Juventus have expressed an interest, while Atletico Madrid have been reportedly linked with a move for Pulisic, who is keen on securing more regular football ahead of the World Cup.
Chelsea's willingness to do business will also be influenced by their ability to land a replacement. Having missed out on Raphinha, who joined Barcelona from Leeds United, they have allowed Timo Werner to rejoin RB Leipzig and Romelu Lukaku to return to Inter Milan, both on loan.