The on-loan star has revived his career since joining the Hammers on loan in January, scoring six goals and providing four assists in just eight games.
Ole Gunnar Solskjaer meanwhile is a keen admirer of Rice.
Now The Athletic claim United are keen to discuss a swap deal involving Lingard, in order to persuade the Hammers into selling their star man.
West Ham didn't include any purchase clause in their loan deal for Lingard, but manager David Moyes is determined to land him on a permanent deal.
Though the Red Devils extended Lingard's contract until the end of next season back in December, it is believed Solskjaer would now prefer to sell the attacking midfielder now his value has increased.
It could take a big bid to lure Rice away from the Hammers though, especially if they achieve Champions League qualification.
This article was most recently revised and updated 2 years ago