The Hammers swooped to appoint Moyes as their new manager on Tuesday, with the Scot arriving just 24 hours after predecessor Slaven Bilic had been sacked.
Moyes arrives with West Ham really struggling having picked up just two wins so far this season, and whilst he will be looking to give everybody a clean slate, he may also have one eye on potential January signings.
The Mirror now report that West Ham are looking to bring in one of Moyes' former players, with the new Hammers boss holding an interest in signing Everton wide man Kevin Mirallas.
Moyes landed Mirallas from Olympiakos back in 2012, and the Belgian winger hit nine goals in his solitary season with Moyes, before the Scot moved on to Manchester United.
Mirallas has now hit 38 goals in 182 games for Everton, but he was frozen out under Ronald Koeman this term, and the report even notes that he was sent away from training by caretaker manager David Unsworth last week.
Mirallas appears set to leave Everton, and it's claimed that Moyes will make a move for the 30-year-old if given any encouragement by his former club.
Signing Mirallas may feel somewhat similar to the signing of Marko Arnautovic; a Premier League winger with inconsistent end product and application past his best, and Hammers fans may have some concerns if Moyes does move for Mirallas.