The England international has been in prolific form at West Ham since being loaned out by the Red Devils in January, scoring eight goals and registering four assists in nine appearances.
Lingard capped another impressive performance for West Ham on Sunday, scoring two goals in a 3-2 victory over Leicester City.
ESPN reports that the 28-year-old has caught the eye of Real Madrid, PSG and Inter Milan, who are all currently monitoring the attacker ahead of a potential transfer this summer.
Lingard only has one year remaining on his contract at Old Trafford, but the European heavyweights will have to compete for his signature with West Ham, who are keen to sign the midfielder on permanent basis.
West Ham currently sit fourth in the Premier League table, putting them on course to qualify for next season's Champions League. body check tags ::