West Ham's assistant boss Peter Grant said: "We have made contact [ and indicated] we are interested. We would be delighted if someone like Roy Keane was available and interested in coming to West Ham United.
"We definitely hope it could happen. We would love the opportunity to speak to him and if he gave us the nod we would be in there for sure.
"The decision comes down to Roy and where he wants to play his football. Does he want to move to London? Does he want to move abroad? Does he want to move to Scotland? If he says he wants to go to Glasgow then it is a waste of time pursuing it because there is only one team he is going to play for.
"But if Roy decides he wants to come to London - then bang, we're in for him.
"The one thing Roy has got is a winning mentality and that is what we are striving for here," said Grant. "Alan said last week how highly we rate him. Someone like that would give the club a huge lift.
"People say things about his team spirit - but that comes down to the fact he wants to win games of football. I don't find that a fault in anybody. That mentality comes from Sir Alex Ferguson - second place is first loser - and that is why he has been so successful in his career. Roy has never accepted second best and we are trying to instil that in our players."
The Beeb:
Earlier on Wednesday Saudi Arabia club Al Ittihad confirmed Keane would not be joining them. despite a short-term offer from the Asian champions.
"We approached the player but because of the rules in Europe, where the contract must be at least six months, the deal was not legal," said club president Sheikh Mansour Al Balawi.