The defender is out of contract in the summer of 2016 and Manchester United are lurking.
He told his weekly press conference earlier today, as reported by the Daily Mail, that Clyne needs to make his decision in the next week and a bit:
"We’re still speaking with Clyney and his agent, but of course we have to know in 10 days.
"The club is doing an offer the maximum what we can do and then we expect the player’s answer.
"I’ve spoken to Clyney, he’s very happy and of course there is some interest but nobody has really bid for the player. All the players are happy with how the team is doing.
"But it’s football, you never know. In football if you go in your last season of contract, we don’t like that.’
"Ask him, ask his agent, I don't know."
Clyne has had a great season at Southampton. He has established himself as one of the top right-backs in the Premier League as well as the number one choice in the position for the England national team.
But that form has not gone unnoticed. Manchester United are in need of a right-back, as Rafael has failed to win over Louis van Gaal and Antonio Valencia is currently playing the position.
Clyne has therefore emerged as a target to join former Southampton team-mate Luke Shaw at Old Trafford.
It was reported by ESPN just yesterday that Manchester United were hoping for Clyne to reject his contract offer at Southampton.
Clyne, who arrived at the club from Crystal Palace in 2012, is currently under contract until next summer so any rejection now would likely see him sold in the summer.