Bale is an odds-on favourite to win the PFA's Player of the Year award after a season which has so far brought 24 goals for club and country.
Bale's recent run of nine in seven games has given Spurs a seven-point cushion in the race for a top-four finish and a place in the last 16 of the Europa League, and Andre Villas-Boas has been forced to field persistent questions about his prized asset's future.
Dawson told TalkSPORT: "Tottenham have got to keep Bale.
"You have to keep all of your best players if you want to be playing in the Champions League regularly and fighting to finish as high as you can in the Premier League.
"Gareth has been brilliant. He's been linked to here, there and everywhere, but when a player is playing as well as he is, that's going to happen. He's a Tottenham player and long may that continue."
Bale was pictured at Old Trafford for the second leg of Manchester United's Champions League tie with Real Madrid on Tuesday, but United have made it clear he was not there as a guest of the club.