The 30-year-old, who made 41 appearances at centre-back for Spurs last season, has been the reported target of interest from Premier League sides Hull City and Crystal Palace.
But Dawson, who has a year of his current deal left to run, said he wanted to be part of a Spurs push for the top four under new manager Mauricio Pochettino.
"I've been at Tottenham for nine-and-a-half years," Dawson, who joined the club from Nottingham Forest in January 2005, told talkSPORT.
"It's a great football club and I've loved every minute of it while I've been here.
"The fans have been superb to me since day one because I've had some ups and downs like everyone does
"The expectations are high and the players want to achieve them. We want to be in the top four and hopefully next year we'll have another push."
Dawson has made more than 300 appearances for the club and won four caps for England, the last of which came in March 2011.