Perch has only recently returned to first-team duty after being sidelined since last April with a stress fracture in his shin.
The 24-year-old has made four appearances since the turn of the year and has now been the subject of a bid from Forest's Coca-Cola Championship rivals.
Davies is not prepared to sell the defender and is unhappy that the details of Newcastle's failed offer have reached the public domain.
"We must be doing something right if other teams in our division want our players," Davies told the club's official website. "But we are looking to build a squad at the City Ground rather than dismantle one and James is not leaving.
"Newcastle's offer for someone we value so highly as a player and an individual was derisory and I'm disappointed it made it into the public domain. That's not our way of doing business."
Perch came through the ranks at the City Ground and has made more than 200 appearances for the East Midlands club.
Meanwhile, United hope to conclude a deal for Manchester United full-back Danny Simpson in the next 24 hours as manager Chris Hughton closes in on his first transfer window breakthrough.
It is understood the 23-year-old, who played the final game of his loan spell in Monday night's 2-2 Coca-Cola Championship draw with West Brom, is due to undergo a medical on Tyneside today.
However, neither the transfer deal nor his personal terms have yet been finalised and the relevant parties remain locked in talks.
Simpson has played a major role in Newcastle's rise to the top of the Championship table, where they stand three points clear of second-placed Nottingham Forest with a game in hand.
He has made 22 appearances and his retention has been one of Hughton's main priorities this month.
Should the Magpies be able to push through a move, that would come as a boost after seeing top targets Jermaine Beckford and Matthew Kilgallon opt to stay with Leeds and Sheffield United respectively.
There were fears last week the deal might not be done after talks stalled, but there is now a new optimism on Tyneside they could get their man after all.