The Hoops have denied the allegation by Tony Mowbray who left his position as Celtic boss 12 months ago before pitching up at Boro in the autumn.
The former Hibernian and West Brom boss says he had other opportunities before assuming control at The Riverside and that he wrote off £350,000 in order to accept the Boro position.
"I had three or four other offers before the Middlesbrough job came along. At the time, I was owed a lot of money by Celtic and they weren't prepared to do a deal to allow me to take those jobs, so I didn't take them," Mowbray told a meeting of Boro fans at a question and answer session.
"I thought they were being unfair but I waited. Then the Boro job came up and I was interested. I wanted to get back to work."
However, a Celtic spokesman responded to Mowbray's claims by saying: "We are very surprised at these comments. Only one formal approach was made regards Tony and that was from Middlesbrough. We blocked no other approaches."