The Tigers captain made 43 appearances in all competitions as the club reached the FA Cup final and finished 16th in the league and is now keen to commit his future
Davies moved to the KC Stadium from Birmingham City a year ago and turned in a series of superb performances under Steve Bruce.
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Despite having two years left on his existing deal, Davies - whose performances led to calls for him to be involved in England's World Cup squad - is keen to lay down roots in east Yorkshire by penning a new contract.
"There's not been an offer at this stage," he told The Hull Daily Mail.
"I'd like to sit down and talk about a new deal but there's not been an offer put my way.
"That's a little bit disappointing but it's one of those things. I've got two years on my contract so maybe the club sees that as long enough.
"If the opportunity came up I'd love to sit down and discuss my future here but that's not my place.
"I can't force anyone's hand into getting a new contract. That's up to the chairman and the manager.
"I'm hoping there will be talks so we'll wait and see where we go."