The England international had a successful loan spell at West Ham in the second half of last season and was linked with a return to the London Stadium over the summer.
Lingard ultimately remained at Old Trafford, though, and scored his second goal of the season in the final exchanges when he came off the bench during Sunday's affair at the London Stadium.
The attacker's goal proved to be winner for Man United, and the 28-year-old has said that he is focused on 'doing his best' for the 20-time English champions after returning to the club.
"I got a brilliant reception (from the West Ham fans). I had a good time here (at West Ham) but I have to move on with Man United and do my best with Man United," Lingard told Sky Sports News.