The 30-year-old, who has been told that he can leave White Hart Lane, is thought to have stalled on a £5m move to the KC Stadium because the contract offered was not long enough.
"To have secured Jake and brought in Tom Ince and Robert Snodgrass, that shows how far we're progressing as a club," he told the Hull Daily Mail.
"A manager is always greedy. Ideally we'd still like another two or three in, especially with what we've got ahead in Europe.
"Michael I've always liked, there's no disputing that. But at the end of the day, he's Tottenham captain with time left on his contract. It's difficult but it's something we've had a nibble at. We'll see if it happens."
Dawson has made 324 appearances for Spurs since joining them from Nottingham Forest in 2005.