Kinnear told the Nottingham Evening Post: "If someone came in for him with £10million then we would have to look at that because that money could go a long way. But he certainly won't be leaving cheaply.
"The club has turned down £5million already and any fee is going to be far in excess of that."
The Irishman has been subject of interest from a host of Premiership clubs this season including Charlton, Blackburn, Chelsea and Tottenham.
The £5m bid that former Forest boss Paul Hart turned down in the January transfer window included Rohan Ricketts as part-exchange so a bid in the region of £6-8m is likely come the summer.
Reid is likely to win the Forest fans' player of the year award this season and is another of example of the Reds youth academy conveyer belt.