Stoke boss Tony Pulis have long been linked with a move for the 26-year-old, but West Ham are looking for an improved offer, according to The Sun.
Stoke midfielder Matthew Etherington has urged Pulis to sign the West Ham striker.
Etherington said: “It would be a good move for him to come here.
“Given the ideas the manager has and the way the club want to push forward, I’d definitely recommend it.
“Coley is a London boy but it wouldn’t be a problem for him living up here – just as it hasn’t been for me. I’d tell him it was the best move I could have made.”