Reports indicated that Calderwood had been interviewed for the post but Northampton general manager Tony Clarke said: "We can categorically say there has been no approach from Forest.
"Colin is under contract and there is a compensation clause in that contract.
"Were any club to speak to him they would have to speak to us first. There has been no approach in any way, shape or form."
Although not one of the initial front-runners for the job, Calderwood does fit chairman Nigel Doughty's stated requirement of a young manager with some experience already.