The Iceland international attacking midfielder was reportedly a target for Premier League rivals Sunderland during August, but he ended up staying at White Hart Lane.
With an influx of new signings at the club, the 24-year-old faces a struggle to hold down a place in Andre Villas-Boas' side.
Nacer Chadli, Erik Lamela and Christian Eriksen can all operate in either the number 10 position or on the left flank, where Sigurdsson enjoyed so much success in the second half of last season.
However, Sigurdsson insists the prospect of moving on never crossed his mind.
"I wasn't close to leaving," Sigurdsson said.
"I came here to play for a big club. When I joined, I knew there would be loads of players and competition.
"You can either be unhappy and leave, or look at it as a challenge.
"Hopefully you'll improve and fight for your place as you know if you do the right thing every day, things fall your way and I'm hoping that will happen."
Sigurdsson had two new signings to thank for helping him score his first two goals of the season last Saturday.
Eriksen, a £11.5million signing from Ajax, laid him on for his first and Brazil international Paulinho supplied the pass that led the Icelandic star to kill off the game.
The two strikes against Norwich, and Tottenham's impressive start to the season, suggest that it may not be so difficult for the seven additions to gel with the rest of the squad.
"The first game when everyone was in was a bit quiet but we're back to normal now," Sigurdsson said.
"Everyone knows each other and it's a good and positive dressing room. There are quite a few jokers.
"We are all of a similar age which helps with the players coming in. It makes them feel welcome and part of the group."
Sigurdsson is expected to retain his place in the Spurs starting XI for Thursday night's Europa League home game against Norwegian minnows Tromso.
But with a total of three games in six days, manager Andre Villas-Boas is likely to give a number of his fringe players a start.