The Sun says Lingard has been in stunning form over the past few months since joining West Ham on loan until the end of the season.
Ole Gunnar Solskjaer has been hugely impressed with his performances, and is a long-time fan of the 28-year-old despite freezing him out.
And United will assess whether to bring him back into the Old Trafford fold before the summer, while not ruling out giving him a new deal.
He has a little more than a year left on his £100,000-a-week terms, and the club could be willing to offer him a new three-year contract.
That would keep his transfer value high while also being able to get him back into Solskjaer first-team plans.
However, it is believed West Ham will try and land Lingard on a permanent move at the end of the campaign after helping their European push.
The Hammers value him between £15million and £20m, but Old Trafford chiefs would want more than that if a deal was to be struck.