Hull boss Steve Bruce has wanted the Spurs club captain all summer and revealed on Sunday that his club had agreed a deal "in principle" to sign the 30-year-old England international.
Bruce previously believed he had lost out on Dawson after holding talks with Tottenham last month, but Sky sources learned last Friday that Hull had moved for Dawson again after Spurs activated an £8m release clause for Sevilla centre-back Federico Fazio.
Speaking after Hull drew 1-1 at home to Stoke City on Sunday, Bruce said: "We hope we can get Michael Dawson.
"There's a deal in place in principle anyway. Hopefully, touch wood, we'll see what develops."
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 made club captain following the retirement of Ledley King in 2012.
Sky sources understand Tottenham are continuing discussions with Argentina international Fazio and are confident of completing a deal to bring the Sevilla captain to White Hart Lane very soon.
Fazio skippered Sevilla to the Europa League last season, captaining the side whilst making 38 appearances in all competitions.