Town are thought to have accepted a bid containing around £750,000 upfront for the keeper earlier this week so they could cash in on the former Wimbledon man rather than risking him leaving on a free at the end of his contract next June.
Speaking to the East Anglian Daily Times, the former Luton Stopper said: "I have met with Mick McCarthy but things are not clear cut and I have not signed anything as yet."
Davis is understood to be concerned about his chances of being the number one goalkeeper at Sunderland next season with current stoppers Thomas Myhre in talks over a new deal at the club and former Derby keeper Mart Poom about to return from injury.
Meanwhile Sunderland are set to hold further talks with midfielder Tommy Miller after he returns from his honeymoon which starts next Monday.