The Iceland international enjoyed a stunning loan spell at Swansea last season, scoring seven goals in 19 games, but has struggled to replicate that form at White Hart Lane following a summer switch from 1899 Hoffenheim.
McDermott confirmed the Royals were knocked back three time by Spurs and were prepared to smash the clubs transfer record with a £10million offer for the 23-year-old to bring him back to the Madjeski Stadium, where he started his career in 2008.
“We sat around last night, we tried to do a deal and we couldn’t do it,” he told BBC Radio Berkshire.
“It didn’t happen,” added McDermott. “We made three offers and you have to give credit to the owner because he tried to make that happen for us and we couldn’t quite get it over the line.
“We were all excited about the possibility of Gylfi coming back but unfortunately he is a Tottenham player and he is a good Tottenham player.”
Sigurdsson has started just six games for Andre Villas-Boas side this term and emerged as a target for Reading boss McDermott after moves for Blackpool’s Tom Ince and Chelsea veteran Yossi Benayoun were shelved.
Owner Anton Zingarevich even went to the lengths of extending his stay in England to try and make the deal happen before the Premier League transfer window closed, but it was to no avail.