Sullivan said yesterday that he felt “depressed” at the lack of new arrivals this summer, but the Hammers have tabled a bid for Fofana worth £25m, plus £11m in add-ons.
West Ham have targeted England defender James Tarkowski, but Burnley want around £40m and Sullivan has said they will not blow their remaining transfer budget on him.
Moyes is targeting a new centre-back and Fofana, a 19-year-old French defender, has emerged as another option.
He made 24 appearances for Saint-Etienne last season as they qualified for the Europa League and made the French Cup Final under Claude Puel.
Fofana has told Saint-Etienne he wants to leave to play in the Premier League. He is also a target for Leicester.
Sullivan has warned West Ham may end the transfer window without any new signings, despite selling Grady Diangana to West Brom for £18m to reinvest the money in the squad.
Speaking yesterday, Sullivan said: “I cannot say for sure that we are going to sign anyone. As each day passes I get more depressed, there is no point in saying otherwise. We are not Roman Abramovich, we are not the king of Abu Dhabi who owns Manchester City. We’re short of defenders.”
Meanwhile, Moyes will remain in charge of the West Ham team remotely against Wolves this weekend if he gets conformation that he must continue to self-isolate.
Moyes, together with Issa Diop and Josh Cullen, was sent home before Tuesday’s 5-1 Carabao Cup win over Hull after returning positive coronavirus tests.
The Hammers boss must isolate for at least 10 days unless further testing returns false positives. Moyes is set to miss Sunday’s game at Wolves and his assistant manager Alan Irvine is set to take his place on the touchline.
But Moyes will remain in contact with Irvine remotely by phone while he watches the game on television at his London home.
Sullivan said yesterday that Moyes had been suffering with a sore throat but that the Scot was in “fine form”.
Moyes is determined to continue working remotely and will help Irvine oversee preparations for the trip to Molineux, starting today when the West Ham players were due to return training after being given yesterday off.
Moyes oversaw the West Ham squad on Zoom during lockdown and wants to keep a close eye on preparations for the Wolves games as the Hammers bid to get their season up and running in the Premier League after defeats against Newcastle and Arsenal.
Sullivan said yesterday: “The manager actually was on fine form this morning.He has had a slight sore throat for a couple of days, but he put it down to the fact that he shouts a lot.”