McDermott had been earmarked by Wolves owner Steve Morgan and chief executive Jez Moxey as a leading candidate to replace the sacked Mick McCarthy, but Reading's new prospective owner, Russian billionaire Anton Zingarevich, is understood to want to keep hold of McDermott if at all possible via a new long-term deal.
McDermott is currently only on a one-year rolling contract, which is part of the appeal to Wolves as he would only cost them around ?500,000 in compensation should he opt to leave Reading.
He joined Reading as their chief scout 11 years ago before eventually becoming Brendan Rodgers' successor as manager in January 2010 after a successful spell in a caretaker role.
McDermott led Reading to the npower Championship play-off final last season before losing to Rodgers' Swansea. But they are mounting another strong promotion challenge during the current campaign despite the loss of key players Shane Long and Matt Mills to West Brom and Leicester respectively last summer.
If McDermott opts to stay at the Madejski Stadium, it will be another blow for Morgan and Moxey after McCarthy's reign was ended nine days ago via a split boardroom vote.
Their initial target, Alan Curbishley, rejected the chance to take charge at Molineux after holding talks, although on Tuesday night he surprisingly re-emerged amongst the leading bookmakers' candidates.
Neil Warnock, with whom Wolves also made contact, opted to take charge at Leeds after his recent dismissal as QPR manager.
A compensation figure in the region of £2million has also cooled Wolves' interest in Brighton manager Guy Poyet, who is less than 12 months into a five-year contract.
Steve Bruce remains the bookmakers' favourite to replace McCarthy and fits the criterion initially laid down by Moxey of having Premier League experience, via Birmingham, Wigan and Sunderland. But Bruce, who has just relocated in the midlands, is becoming increasingly frustrated that no further contact has been made with him since he was interviewed last Friday.