David Moyes is keen to add at least one central defender before the window closes at the end of the month.
West Ham have been in talks with Chelsea over a deal for Zouma in recent weeks and the Blues are willing to offload the 26-year-old for around £25million.
But the deal has stalled over his wage demands of more than £100,000-a-week.
West Ham are operating on a limited transfer budget this summer and Zouma, who is under contract until 2023, is likely to need to drop those demands for a deal to happen.
Zouma is free to leave Chelsea this summer having fallen down the pecking order at Stamford Bridge under Thomas Tuchel.
Tuchel handed Trevoh Chalobah his Premier League debut ahead of Zouma against Crystal Palace on Saturday and the 22-year-old impressed and scored a fine goal.
Fiorentina defender Nikola Milenkovic was a target for West Ham before talks with the Italian club ended last week.
Burnley centre-back James Tarkowski was a top target for Moyes last year but it is understood the 28-year-old is keen to see out his contract at Turf Moor and move on a free at the end of the season.
Craig Dawson and Angelo Ogbonna started at in central defence for the West Ham in their win at Newcastle on Sunday but Moyes was frustrated by defensive mistakes in the first half and, with Europa League football this season, remains keen to bolster at the back.
West Ham have loaned Frederik Alves to Sunderland, while Issa Diop and youngster Jamal Baptise were on the bench at Newcastle on Sunday.
"When I took Frederick Alves I felt I had to have a look at him for six months to see what he can do and if he was not going to affect the first team then he would go out on loan," Moyes said at the weekend.
"I have 17-year-old centre-half Jamal [Baptiste] who I want involved in the first-team training but undoubtedly I am going to try and add to the squad I am and I will be adding a defender and maybe other players as well but then if I don't then I will be happy if the players perform as well as they did.
“If the players perform as well as they did last season and today then it means whoever we bring in has got to be at a very good level.”
Moyes is also keen to add a striker to support Michail Antonio before the end of the month.