The Croatian is facing the axe following the 4-1 home defeat by Liverpool on Saturday.
Moyes, the former Everton, Manchester United and Sunderland boss, used a television appearance to make it clear he was standing by to take over.
“I’m interested, yes,” he told beINSPORTS. “I’ve had no contact from West Ham but I’ve always said I want to go back into club management. If the right opportunity comes around I’d be interested.”
The Scot added: “For me to get back in it means another manager is going to have to lose their job and I wouldn’t wish that on anybody.” Moyes has also been linked with the vacant Scotland job but sees that assignment coming later in his career.
“Certainly one day I want to manage Scotland, if I’m lucky and fortunate enough to do it,” he said. “I don’t know if it’s right for me just now, I think my preference is to go back into club management. If club management didn’t come along for me I might look at it differently.”
Everton climbed out of the relegation zone after coming from two goals down to win 3-2 at home against Watford, who missed a penalty in a 13-minute period of stoppage time. Goals by Richarlison and Christian Kabasele put Watford 2-0 ahead. Oumar Niasse, Dominic Calvert-Lewin and a Leighton Baines penalty turned the game around. Tom Cleverley missed a penalty for Watford in the 101st minute.
A goal from Son Heung-min saw Tottenham beat Crystal Palace 1-0 at home.