Manolo Gabbiadini of Southampton battles with Lewis Dunk of Brighton and Hove Albion
The Hammers appointed Moyes as their new manager last week following the departure of Slaven Bilic, and the Scot will be looking to get off to a strong start against Watford this weekend.
Having taken the job well in advance of the January transfer window, Moyes has two months to evaluate his squad and decide where he needs to strengthen.
The Mirror report that he already has his top target identified, with Brighton and Hove Albion defender Lewis Dunk allegedly eyed up as Moyes' preferred first signing.
Dunk, 24, was born in Brighton and came up through the ranks with the Seagulls, featuring in League One all the way up to the Premier League throughout their journey.
The 6ft 4in centre back has now racked up more than 200 appearances for Brighton, and he has transitioned seamlessly into Premier League life with some superb displays for Chris Hughton's men.
Lewis Dunk of Brighton and Hove Albion and Nikola Vlasic of Everton
Dunk particularly impressed against West Ham last month, and his performances have seen many call for him to be called up to the England squad.
Now, West Ham want to add a younger centre back to compete with veterans Jose Fonte and James Collins, with Dunk fitting the bill – and given that new Hammers coach Stuart Pearce worked with Dunk for the England Under-21's, a January bid seems likely.