The Sun says United are considering handing Lingard a shock new deal – by triggering his one-year option.
The midfielder, 27, is out of contract next summer, with Ole Gunnar Solskjaer considering offloading him.
The England ace has been eyed by a number of Premier League clubs, including Everton and West Ham.
Lingard has also been strongly linked with Tottenham.
But United are looking to extend his contract by a further 12 months, to make sure his market value of £25million is kept.
Old Trafford chiefs are planning to exercise their option within the next few weeks.