The 28-year-old's current deal is due to expire this summer, but the club have not made an official approach - although it is understood they were considering offering him a new deal on reduced terms.
But with clubs from the Premier League and Championship having already expressed an interest, Bailey is considering his options elsewhere.
"I've never said I wanted to leave Middlesbrough," the midfielder told Sky Sports News.
"I have not been offered anything at Middlesbrough. Life goes on. If I was to leave then I would have had a few good memories. It might be time to move on.
"I would consider a new contract. If it was right for me and the family then 100 per cent I would be there. We will see what happens. Hopefully I will have something sorted soon.
"I'd be really happy to stay and helping Middlesbrough back in the Premier League but I suppose time will tell."
Andre Bikey is another of Boro's out-of-contract players who the club do not look set to offer terms to. The club did have a one-year option on the Cameroon stopper.
Kieron Dyer, Julio Arca and Stephen McManus have already left the club after their deals expired.