The winger moved to London Stadium last Friday on a loan deal that will see him work under David Moyes for the remainder of the season.
Lingard, who did not make a single Premier League appearance under Ole Gunnar Solskjaer in the current campaign, celebrated his league return by scoring a brace against Aston Villa on his West Ham debut en route to a 3-1 win on Wednesday night.
West Ham paid a loan fee of around £1.5m to Manchester United for Lingard’s signature, while also agreeing to cover his £100,000 a week wage.
But the Hammers do not have an option in Lingard’s contract to make his move to the capital club permanent.
The Red Devils were reluctant to include an option to buy in the 28-year-old’s loan deal.
Despite Lingard only clocking up 179 minutes of football across all competitions at his parent club in the current campaign, Manchester United were against the idea of allowing him an option to move on permanently this summer.
Manchester United triggered a one-year-contract extension in Lingard’s contract in December and his Old Trafford stint is now set to run until the summer of 2022.
It remains to be seen whether West Ham will sit down at the negotiating table with Manchester United when the next transfer window opens to talk over potentially adding Lingard to their ranks on a permanent basis.