The right back has just over a year left to run on his contract at St Mary's but Saints director Les Reed is confident he will prolong his stay.
The former Crystal Palace defender has been linked with a move to Manchester United after another outstanding season which has included international recognition for the first time.
Goal understands Clyne, whose current deal expires in 2016, would be receptive to a move to Old Trafford but Reed remains confident he will remain with the Saints.
He told talkSPORT: "We're in constant communication. These contract negotiations are never just one meeting, where everything is done and sorted out.