Hull boss Steve Bruce has made Davies one of his top targets and the Premier League new boys are thought to have agreed a deal with Blues.
Birmingham fended off several approaches in the January transfer window but they are resigned to losing the 28-year-old this summer.
Davies, who was Birmingham's player of the season last term, is keen to get back to playing in the Premier League, and as he is entering the final year of his contract Birmingham are ready to sell him.
Bruce is a big admirer of Davies and sees his Premier League experience from his time at West Brom and Aston Villa as valuable to his squad for next season.
Davies is now expected to hold talks with Bruce in the next few days as he looks to persuade the centre-half to move to the KC Stadium.