The Hammers offered their former player the chance to keep up his fitness over the summer by using the club facilities, following his exit from Nottingham Forest.
At the time, Lingard’s return was seen more as a gesture of goodwill than a serious opportunity for him to earn a contract.
However, Moyes has spoken glowingly of the 30-year-old’s progression since his return to West Ham.
“Jesse has trained with us for three weeks and he’s improved greatly from when he first came in,” he told talkSPORT.
“He’s in really good condition – much better condition than he was when he first came in.
“I have to say, when Jesse joined us two years ago I think he scored nine goals in 15 games and was probably the difference between us getting into Europe for the first time [under me].
“I want to give him every opportunity to get himself back in condition and see how he does.
“So there’s no real update on it at the moment, just to say that he’s back and getting much closer to the levels of fitness where you’d hope he would be.”