Davies moved to the KC Stadium from Birmingham City a year ago and turned in a superb season under Steve Bruce.
Taking over captaincy duties from Robert Koren midway through the campaign, Davies proved to be a rock in Hull's defence as they secured top-flight survival and reached the FA Cup final before losing to Arsenal in extra-time.
Despite having two years left on his existing deal, Davies - whose performances led to calls for him to be involved in England's FIFA 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."
