The 28-year-old England international had struggled to establish himself as a regular at Old Trafford under Ole Gunnar Solskjaer.
The West Ham player has thrived since his arrival at the London club and made an instant impact on his debut as he scored a superb brace against Aston Villa in a 3-1 win.
He also picked up an assist in the first half as West Ham went 3-0 up, only for Arsenal to complete their comeback and secure a 3-3 draw.
Lingard's renaissance at West Ham has been spotlighted in a compilation as the United loanee has been in fine form under Moyes' tutelage.
Former England under-21s manager Stuart Pearce insisted that Lingard "needed a move away from United," saying it has "rekindled him a little bit and he's really enjoying his football."
The West Ham first-team coach told talkSPORT: "He's come and certainly given us another dimension at the club. He's got a great, bubbly personality. He's fit in straight away with the boys.
"I think he needed a move away from United. He wasn't playing and whatever and this has rekindled him a little bit and he's really enjoying his football.
"I've had the conversation with Jesse, shortly after he was here and I've talked to Gareth, and I said, 'There is an opportunity and if your form is good, he always leaves the door open for players.'
"For Jesse, and other players around the Premier League, that maybe weren't in the last squad, John Stones probably falls into that category as well, that are showing good form that Gareth can't ignore.
"I'd be delighted if Jesse's form at our club managed to get him in the international fold again."
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