The Irishman held talks with Scunthorpe United after a £600,000 bid was accepted by Killie for his services, but he eventually snubbed a move to Glanford Park.
Now he is being linked with Celtic.
"I do hear rumours but that's part and parcel of the transfer window with names being thrown about," he told the Daily Record.
"I've no other offer and never had another one. When I went to Scunthorpe it was the only option I had but I didn't feel the move was right.
"I've got 18 months left on my deal and I'm happy to stay at Kilmarnock until the summer at least as I've never tried to get a move away.
"I feel that between now and the end of the season we can keep improving as a team and stay in the top six."