Bullard’s contract with Hull City is set to be terminated following an alleged incident during the club’s pre-season trip to Slovenia.
Bullard has also been linked with the likes of Wolves, Queens Park Rangers and Ipswich.
Kean said: “I’ve probably been linked with Jimmy because I met him on Sunday when he was out with his boy, and I had a chat with him and he was telling me about his troubles, and he could be available.
“I had Bully when I was with Chris Coleman at Fulham, and he is a colourful character.
“But I don’t know how his fitness is, whether he has done a full pre-season. But he is a quality player when he is on his game.
“It depends if we need somebody in that position, and if we have done our business and filled those slots, then it might not happen, but if we haven’t, then you never know.”