Tigers manager Steve Bruce is keen to add to his squad following their return to the Premier League and has moved for the 28-year-old centre-back, who once cost Aston Villa £9m.
The fee that will see him switch Birmingham for the KC Stadium is a reported £2.25m, and Clark has revealed that he expects a deal to be completed without a hitch.
"We've agreed terms with Hull City," Clark told Sky Sports News. "Obviously Curtis and his advisor will be trying to do the same on a personal level.
"Then, he will be going through a medical and that will probably be a formality because he played numerous games for us last season and has got a good appearance record over the past year."
Davies made 41 Championship appearances for the Blues last season, scoring six goals.