Iceland international Sigurdsson, 23, started his professional career with the Royals before moving to Hoffenheim in 2010.
"We tried to bring him back. We had spoken to Spurs and we made three offers," said McDermott. "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."
Tottenham signed Sigurdsson on a permanent deal last summer after the player had impressed during a loan spell with Swansea last season and he has made 30 appearances for Spurs this campaign, scoring two goals.
He played 51 games for Reading between 2008 and 2010, scoring 22 goals.
McDermott also admitted that Reading had lodged a bid for winger Ince before the transfer deadline but this was rejected by Blackpool.