Premier League new boys Hull have agreed a fee, reportedly in the region of £2.25million, for Davies, who has a year left on his contract at St Andrew's.
Davies has been holding talks with the Tigers on Monday and Clark is not anticipating any issues with the transfer going through.
"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 has featured over 100 times for Birmingham since joining the club in January 2011 from Aston Villa and has also played for West Brom.
He was linked with Norwich City and Wolves in the January transfer window, but is now poised to return to the top flight with promoted Hull.