Javier Hernandez is currently West Ham's top goalscorer with four goals this season.
The 29-year-old was replaced in the 51st minute of Mexico's 3-3 draw against Belgium last Friday, and has since withdrawn from Juan Carlos Osorio's side in order to have a chance of being fit for the Hammers.
However, The Times report claims Hernandez underwent a scan on Monday after appearing to injure his hamstring in the green of Mexico. However, the results showed inflammation on his thigh.
With four goals in his 13 West Ham appearances, the former Manchester United striker is the Hammers' top goalscorer so far this season but is yet to find the back of the net in a match that the east Londoners have won.
Now, Moyes will be sweating on the fitness of his star striker as he looks to get off to a winning start with West Ham sitting in the bottom three of the Premier League after losing to Liverpool 4-1 last time out.
West Ham fans were devastated on Twitter after hearing that Hernandez could miss Sunday's Premier League clash, with some fans urging Moyes to start striker Diafra Sakho instead.
At least Sakho scored so he could come in now under Moyes— matthew woodall (@woodall_matthew) November 11, 2017
Going to have to get Sakho on board!— DRG (@dgolledge) November 11, 2017
Nightmare— Ian Culley-Morgan (@seevic) November 11, 2017
Perfect excuse for DM not to play him. Hoof ball is the only option.— Mick Pirlo (@frenchie1309) November 11, 2017
He’s caught westham— Mark (@ElvinWestside) November 14, 2017
precaution hopefully...— Will Mason ⚒ (@WillMason94) November 13, 2017