The Royals had three separate bids rejected for their former player and were willing to make the Iceland international their record signing, but were unable to strike a deal
The Iceland international, who came through the ranks at Reading, has struggled to hold down a first-team place at Spurs following his move from Hoffenheim in the summer, and McDermott has confirmed the club came close to re-signing the player on Thursday night.
"We tried to bring him back," McDermott told reporters. "We had spoken to Spurs and we made three offers.
"I thought at one stage we had a real chance of doing a deal, but unfortunately, we couldn't manage to do it. Gylfi is a Tottenham player, but we've know him since he was 13 years old and it would have been great to bring him back."
Sigurdsson has made 21 league appearances for Tottenham this season, but 15 of them have come off the bench.