Cole had started training with his former club earlier this week and had seemed set to re-join the Premier League side.
However, Jack Sullivan, the son of co-chairman David Sullivan, has revealed that Cole's fitness is an issue.
"Cole is not fit enough to offer a contract to," revealed Sullivan.
"But he's thinking over getting fit with us and improving his fitness."
Sullivan confirmed Sam Allardyce's side are in the market for other free agents and said: "We are also looking at other non-contract players."