Carroll has also been linked with a move to former club Newcastle United and the striker is not sure what the future holds past the end of the season.
"I have just got to wait and see, really," he said. "We'll see what happens at the end of the season.
"Obviously I don't know what is happening so we will just have to wait and see.
"It has been great here and every minute has been fantastic. The lads have been great, the gaffer has been great and the fans are unbelievable."
Asked whether he would stay if West Ham put the right money on the table, he added: "We will have to wait and see. It is obviously a great club and I do not see why not."