Hull boss Nigel Adkins hopes to complete most of his transfers before pre-season training starts on 25 June.
Hull have struggled to complete deals early in recent seasons, making five signings in the last 10 days of the 2017 summer transfer window.
The Tigers have lost six senior players this summer and have yet to make their first signing since last season ended.
"Over the last several years we've left it until the last minute which I don't think is ideal," Adkins said.
"I'd like to think over the next week to 10 days, or before we come back to training, a lot of things that we've been doing behind the scenes will start to come to fruition in terms of people putting pen to paper."
Adkins confirmed that full-back Moses Odubajo has left the club after rejecting a new contract, while out-of-contract midfielder Max Clark has attracted interest from Vitesse Arnhem, who are managed by former Hull boss Leonid Slutskiy.
"I'd like Max to stay, I know there is interest from Vitesse Arnhem," Adkins told BBC Radio Humberside.
"There have been no bids on the table whatsoever, there has to be a compensation paid. Max is a young player and we'd like him to stay."