The Hammers left-back was forced off at Manchester City last weekend after colliding with the goalpost when blocking a shot and missed Wednesday’s night draw against Brighton.
Ben Johnson deputised on the left of a back four but the east Londoners missed the balance and threat Cresswell offers down that side.
The 31-year-old has been doing light training this week but David Moyes must make a late call over his fitness.
“Aaron Cresswell is back in training, he’s done a bit of light training, so we’ll have a look at that,” Moyes said.
“After that, most of it is pretty much okay. Obviously we had the bad news on Angelo Ogbonna, who did his cruciate a few weeks ago, but in the main we’re pretty close to getting everybody fit.”
West Ham predicted XI: Fabianski; Coufal, Zouma, Dawson, Johnson; Rice, Soucek; Bowen, Benrahma, Fornals; Antonio.
Date: Saturday, December 4, 2021. 12.30pm GMT, BT Sport
West Ham squad from: Fabianski, Martin, Randolph, Areola, Diop, Dawson, Zouma, Baptise, Coufal, Johnson, Ferdericks, Masuaku, Rice, Soucek, Noble, Kral, Vlasic, Yarmolenko, Fornals, Lanzini, Benrahma, Bowen, Antonio.
Doubtful: Cresswell (back)