Lingard, 28, has scored six goals in eight games for the Hammers since arriving on a season-long loan deal in January.
The deal did not include an option to buy but David Moyes has made it clear that the Londoners are keen on signing Lingard on a permanent basis, with a senior source at the club insisting they’ll do ‘whatever it takes’ to make it happen.
Lingard will have a year to run on his deal by the end of the season but United value the England international at around £30m, which could prove prohibitively high for West Ham.
But the Athletic claim the Red Devils could use Lingard as a makeweight in a bid to sign Rice.
The England midfielder has taken his game to new levels this season after being denied an £80m move to Chelsea last summer.
Ole Gunnar Solskjaer is a huge admirer of the defensive midfielder and believes that he could be a long-term replacement for Nemanja Matic, who turns 33 in August.
While West Ham would be desperate to keep Rice, they may struggle to do so should they fail to finish in the top four.
The Hammers now value Rice at more than £100m, which United would not consider bidding.
But including Lingard in a deal to move the opposite direction could make sense for both parties, with Rice determined to play Champions League football next term.
United are yet to make a final decision on Lingard’s future and the Red Devils may even offer the midfielder a contract extension in order to obtain a larger fee for the playmaker.
Lingard, for his part, hasn’t given up hope of returning to Old Trafford but he’s happy at the London Stadium and knows his chances of first team football are better in the capital.