The Hammers needed midfielder Cheikhou Kouyate to bag the equaliser after Marc Albrighton's opener, but remain in the relegation zone after a poor season to date.
With goals still something of a problem for West Ham, Moyes may look for attacking reinforcements in attack, especially with question marks over the future of Diafra Sakho coupled with Andy Carroll's goalless season to date.
Another physical target to lead the line or possibly link up with Javier Hernandez could be appealing if Sakho does move on, and The Mirror report that Leicester City are willing to sell former Moyes target Leonardo Ulloa in January.
As reported by Sky Sports, Moyes attempted to bring Ulloa to Sunderland in January, but the Foxes stood firm, rejecting three Sunderland bids only to limit the Argentinian's playing time anyway, now leaving him behind Jamie Vardy, Shinji Okazaki, Kelechi Iheanacho and Islam Slimani in the pecking order.
Ulloa may be a player that Moyes likes, and he could offer another goal threat for the Hammers, meaning rekindling his interest could make some sense if he is working on a tight January budget – but Moyes may find that West Ham fans expect a higher profile addition.
The Hammers brought in the likes of Joe Hart, Pablo Zabaleta and Javier Hernandez over the summer, landing big-name Premier League performers who had won trophies with major clubs, and Ulloa may not exactly set pulses racing.
Whilst Moyes keenly pursued Ulloa earlier this year – suggesting he may still be on the Scot's radar – West Ham should be looking a bigger-profile signing than a Leicester reserve, and even though Moyes' budget may allow him to go and pursue one of his top targets from his time at Sunderland, he now has the chance to aim higher, and should subsequently only consider Ulloa if bigger-name talents can't be landed.