The defender has been informed he is surplus to requirements under new boss Mauricio Pochettino, with a number of Premier League clubs ready to make an offer for the 30-year-old.
The central defender is in the final year of his contract at White Hart Lane and Spurs do not believe he suits new manager Mauricio Pochettino's preferred style of play. He is available for around 6 million pounds.
Hull has already shown it is ready to spend big this summer, having already shelled out a club record transfer fee for Jake Livermore ahead of its first European campaign, and it is believed the club is prepared to pay 4 million pounds for Dawson.
But former Spurs boss Harry Redknapp wants to reunite with his former captain, two years after Dawson turned down a 9 million pound transfer to Loftus Road, and QPR is understood to be the slight favorite for the 30-year-old.
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Dawson, who made 41 appearances in all competitions for the North London outfit last season, joined Tottenham from Nottingham Forest for 4 million pounds in 2005.
While Dawson has been told he is free to leave the club, Tottenham is less willing to let Argentine winger Erik Lamela leave.
The 27.5 million pound signing from Roma made just 17 appearances for Spurs during a difficult debut season, which culminated in his omission from the Argentina squad for the World Cup.
Reports have linked the 22-year-old with a move back to Serie A to kick-start his career, but advances from Inter have so far been rejected.