Harry Arter of AFC Bournemouth celebrates victory against Newcastle United
Moyes, 54, has arrived at the London Stadium to replace Slaven Bilic, who was sacked on Monday after a 4-1 home defeat at the hands of Liverpool on Saturday.
The Scot will be looking to give his players a chance to shine before the January transfer window, but after struggling so far this season, Moyes may also have transfer targets in mind.
Republic of Ireland's Harry Arter (L) takes on Moldova midfielder Eugen Cebotaru (R)
Now, The Mirror report that West Ham are interested in signing Bournemouth midfielder Harry Arter, in a bid to boost Moyes' options in the middle of the park.
Arter, 27, started his career in the youth ranks of Charlton Athletic, but moved on to Woking in 2009, rebuilding his career in non-league before earning a 2010 switch back into the Football League with Bournemouth.
The midfielder has now racked up over 200 appearances for Bournemouth, becoming a key part of Eddie Howe's midfield at the Vitality Stadium, and he has featured in seven of the Cherries' 11 Premier League games this term.
A Republic of Ireland international with six caps to his name, Arter's tireless displays in the Bournemouth midfield appear to have attracted West Ham's interest, and they want to hand him a return to London.
Moyes will have Pedro Obiang, Mark Noble and Cheikhou Kouyate at his disposal, but Arter would add depth to the West Ham midfield, presumably without breaking the bank, though Bournemouth are in a strong position given that he is under contract until 2021.