Full-back Cresswell picked up a back problem during Sunday’s defeat at Manchester City, which saw him substituted during the second half, but has been able to resume training.
Defender Angelo Ogbonna is starting his rehabilitation from a long-term knee injury, which is set for surgery.
West Ham are fourth in the table but looking to get back on track after successive losses to Wolves and Man City.
The experienced Moyes however is delighted with the season overall and says it's been his best start as a Premier League manager.
"It's right up there with the best (starts to the season)," said Moyes.
"I think the big thing I've got is a really good team - a group of players who are competitive, working on changing the mentality, and I think when it comes to 28 December, I'll have been here two years. The turnaround the players have made in that time has been great, so they deserve huge credit for what they've done.
"I'm still trying to build the club. 18 months at the moment isn't a long period to be at any club, but the players - and us as a staff - have made decent progress."
Brighton striker Aaron Connolly could make his return to the Brighton squad at the London Stadium.
The Republic of Ireland forward, absent for the Seagulls’ last four matches, has been recovering from a heel issue.
"He’s in contention," said Albion boss Graham Potter. "He has suffered a little bit with injury, with loss of form, a little bit of confidence, a little bit of everything.
"He’s had a bit of what Neal has had, criticism of when he’s missed or chances that have got away from him.
"But he’s 21-years-old, we forget that they’re still learning to be top players in a top league, he’s not the finished article. He’s working hard, he’s supporting the team, he will be in contention for Wednesday."
Of West Ham's progress this term, the Albion head coach added: "It’s always tough playing against West Ham and the job that David Moyes has done is obviously fantastic.
"To be in Europe, they’ve won their group and they’re in the top four of the Premier League, it’s amazing.
"When you have that type of opponent it’s a challenge, we’ve had good performances up there, we have to go and play well, but our challenge is to maintain the performance level that we had against Leeds United, if we do that we give ourselves a chance in the game."
Albion forward Danny Welbeck (hamstring) and midfielder Steven Alzate (ankle) are expected to be training with the team again over the next couple of weeks.
West Ham provisional squad: Fabianski, Cresswell, Zouma, Dawson, Masuaku, Johnson, Fornals, Soucek, Rice, Antonio, Benrahma, Areola, Coufal, Diop, Kral, Lanzini, Vlasic, Noble, Yarmolenko, Bowen.
Brighton provisional squad: Sanchez, Steele, Lamptey, Cucurella, Webster, Dunk, Duffy, Burn, Veltman, Bissouma, Mac Allister, Mwepu, Gross, Lallana, Moder, March, Richards, Connolly, Maupay, Trossard, Locadia, Sarmiento.