Dawson, 30, has been a target for Tigers boss Steve Bruce all summer but he previously believed he had lost out on the England centre-half after discussions reached a dead end in July.
The England capped centre-half has one year remaining on his contract and was thought to be reluctant to leave a club that was a year away from awarding him a 10-year testimonial.
But with Spurs in discussions with Sevilla to sign their captain and star centre-back Federico Fazio, having failed to sign his Argentinian compatriot Mateo Musacchio of Villarreal, Hull have renewed hope of landing Dawson.
Sky Sports reported earlier this month that Tottenham had identified Musacchio, 23, as the man to improve their back-four but those discussions reached an impasse with the player’s third-party ownership.
Instead they have turned their attentions to Fazio, with Sky sources learning on Thursday that Spurs were interested in bringing the twice-capped Argentina international to White Hart Lane, and Sevilla manager Unai Emery strongly suggested on Friday that the club had already met his £8million release clause.
Emery has been forced to omit Fazio, who led Sevilla to the Europa League last season, from his squad to face Valencia in their La Liga opener on Saturday.
And his possible arrival means Dawson is set to leave the club he joined from Nottingham Forest in 2005 and has made over 300 appearances for, scoring 10 goals. He was also made club captain following the retirement of Ledley King in 2012.
Hull, who have signed Tom Huddlestone and Jake Livermore from Tottenham in recent transfer windows, have also had two bids rejected for Blackburn striker Jordan Rhodes.