The Sun says Lingard has rediscovered the form that made him an England regular since arriving at the Hammers on-loan in January.
The star has produced four goals and two assists so far in his six matches for David Moyes' Champions League-chasing side.
And that has convinced his former United manager to try and secure his services long-term at the end of the campaign.
According to ExWHUemployee, speaking on the West Ham Way podcast, he insists the Hammers have a firm belief they can convince him to stay once the window re-opens.
It is also claimed he is loving life with the East London club.
His contract was due to expire in June but the Red Devils have already triggered their option of a 12-month extension.