The 28-year-old midfielder has been an instant hit since joining the Hammers on loan in January, with eight goals and nine assists in nine appearances for the London club.
And he proved his importance to West Ham and their Europe push again this weekend with two goals in a 3-2 win over Leicester.
West Ham will surely do everything they can to keep the recently recalled England international beyond the season, despite Ole Gunnar Solskjaer insisting United expect him back at Old Trafford in the summer.
But the Daily Star claim Arsenal have joined the race for Lingard following his breathtaking return to form in the Premier League.
West Ham don’t have an agreement in place to sign Lingard at the end of the season, and it is claimed he could be snapped up by a rival club for around £30million.