Bale enjoyed a stellar 2012/13 season and picked up three major individual accolades as Spurs finished fifth in the Premier League.
Spurs' failure to qualify for the Champions League has prompted speculation that both Manchester United and Real Madrid will try to sign the Wales international.
Andre Villas-Boas has insisted that the attacker is not for sale and also confirmed that there have been no offers for Bale amid reports United are preparing a £60million bid.
Dawson is not surprised by the rumours concerning Bale, but is not worried about the prospect of Spurs losing their star man during the transfer window.
"All you can do is concentrate individually as a team," Dawson told Sky Sports News.
"Gaz is a Tottenham player and the manager has come out and said he's staying, and that's great news.
"To do what Gaz did last year was sensational, with some of the goals he scored and the points he won for us. He helped us to get to 72 points and I'm sure he'll be doing that again next year.
"Gaz is a great lad, he keeps his head down and the way he has been playing, he is going to have speculation. His performances in recent years have been brilliant and that's what happens.
"He'll concentrate and do what he does for Tottenham, and hopefully keep scoring goals."