Goalkeeper Alisson missed Wednesday night’s Champions League defeat by PSV Eindhoven due to illness.
A muscle complaint meant Wirtz was also absent for that game after being sidelined for the preceding loss against Nottingham Forest too.
Speaking at his pre-West Ham press conference on Thursday, head coach Arne Slot said: “Ali trained again with the team today, so we hope and expect him to be available at the weekend.
“Florian will have his final day of rehab tomorrow. So, if that all goes well, he could train with the team on Saturday.”
Hugo Ekitike started the clash with PSV but was forced off early in the second half due to a back problem.
Slot said of the France international: “They don’t expect that it has to be a big issue, but the games come fast so let’s see for the weekend.
“But it shouldn’t have to be a big issue.”