The Scottish Premier League side say they have had no official approach from the Championship outfit despite reports linking Calderwood with a return to the City Ground.
The Hibs boss has reportedly been targeted by Forest to work as assistant to their new manager Steve McClaren.
A statement from the Edinburgh club read: "Hibernian today moved to address media reports regarding manager Colin Calderwood. The club can confirm that no official approach has been made by Nottingham Forest to the club, and none would be welcomed."
The statement continued: "The manager and team are currently at their pre-season training camp in preparation for the forthcoming campaign."
Calderwood was manager of Forest for two and a half years and led them out of League One before being sacked in 2008.