Bale has been strongly linked with both Manchester United and Real Madrid this summer.
Reports have suggested that United are preparing a massive £60million bid for the highly-rated Wales international.
"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."