Newcastle United, Juventus and Atletico Madrid are all believed to have made approaches to sign Pulisic this summer.
And according to The Athletic, United are set to join that list and test whether the Blues will loan the winger out.
The report adds that Pulisic, 23, is ready to listen to offers to move away this summer and even prefers joining United over anyone else.
It comes following a lack of game time with the Qatar World Cup starting in just three months.
Pulisic was linked with United and Liverpool before signing for Chelsea in a £58million two years ago.
In the period since, he has made 117 appearances, scoring 25 goals.
Last season, he suffered a period on the sidelines following an ankle injury and made just 13 Premier League starts.
He finished the campaign with only eight goals and fell behind in the Chelsea pecking order.
Already this season, Romelu Lukaku, 29, has re-joined Inter Milan on loan and Timo Werner, 26, is back at RB Leipzig permanently.