Sigurdsson, 23, who began his professional career with the Royals, has made just six Premier League starts since joining Spurs from Hoffenheim in July.
However, the London club appear to be determined to hold onto the Iceland international.
"We tried to bring him back," said McDermott. "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 known him since he was 12-13 years old and it would have been great to bring him back."
Reading had been prepared to spend a club-record transfer fee on Sigurdsson.