The Hammers brought in Moyes as their new manager on Tuesday, less than 24 hours after parting ways with Slaven Bilic, with the 4-1 home defeat to Liverpool proving to be his final game in charge.
Moyes will now have the international break to work with his new players in the hope of sparking a turnaround when West Ham take on Watford a week on Sunday.
Moyes may be looking to make January additions despite only having a contract until the end of the season, and The Mirror claim that a new move for William Carvalho is being weighed up.
West Ham wanted to sign Carvalho over the summer before matters turned sour between West Ham and Sporting CP, as reported by the London Evening Standard after the end of the summer transfer window.
Now, it's believe that West Ham are eyeing a new January bid for the midfielder, though they will surely be hoping to smooth over relations with Sporting before making any move – and renewed interest is no huge shock after Moyes' arrival.
As reported by The Mirror in March 2014, Moyes wanted to bring Carvalho to Manchester United in a huge £37million move, and whilst that deal didn't go through after Moyes was sacked, it would be little surprise to see him launch a new bid.
A powerful holding midfielder with composure on the ball and a superb passing range, Carvalho could be the injection of real quality that West Ham need in the middle of the park, competing with Pedro Obiang, Mark Noble and Cheikhou Kouyate - but it could take a huge fee and some relationship work with Sporting to help Moyes finally land his man.