The Welshman has been linked with a record-breaking move to Real Madrid or Manchester United after a series of excellent performances last term, following his adaptation to a move from the left wing to a more versatile central attacking role.
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"All you can do is concentrate individually as a team," he told Sky Sports. "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."
Bale won both the Players’ and the Football Writers’ Player of the Year awards after scoring 26 goals in all competitions last season.
Dawson admits Bale’s performances were always likely to attract attention but feels the forward will continue to impress for Spurs.
"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 commented.
"He'll concentrate and do what he does for Tottenham, and hopefully keep scoring goals."