A Forest spokesman said: "Andy agreed a long-term contract with the club only last season. We've already rejected one bid of £2.5million and the club would be looking for significantly more than that."
Forest chairman Nigel Doughty will be looking for at least £5m - the same fee that Jermaine Jenas comanded when he he transferred to Newcastle.
Reid played during the Republic of Ireland's 2-1 win against Czech Republic on Wednesday night. They won 2-1 thanks to a Robbie Keane winner but Reid was substituted by Rory Delap midway through the second half.