City's player of ther season it appears has been subject to a bid from relegated Forest.
The East Midlands club may come back next week with an improved offer.
Barker started the season at City before a loan spell at Stoke. He was recalled from that and came back a much fitter and better player.
With Tony Vidmar already gone and Gabbidon and Collins on the verge of leaving City can ill afford to lose another top defender.
