Clark featured in Forest's 1979 European Cup-winning side before going on to be manager and chairman at the City Ground.
Burt ends a seven-year association with the npower Championship outfit, having played a key role in Sean O'Driscoll's extensive summer recruitment drive.
O'Driscoll was dismissed as manager following Forest's 4-2 Boxing Day victory over Leeds, making way for Alex McLeish.
When contacted by Press Association Sport to confirm reports of his exit, Clark said: "Yes that's true, yes. I don't want to say any more about it, for obvious reasons, but that is true.
"It's a shock, it's certainly a shock. Right out of the blue - a real shock."
