Clyne is out of contract next summer and fuelled speculation over a move to Manchester United by telling Sky Sports News HQ earlier this month about his desire to play in the Champions League.
The 24-year-old has been one of Southampton’s stand-out performers this season and earned his first England call-up for the Euro 2016 qualifying games against San Marino and Estonia.
Koeman insists the full-back is happy at the club but says Southampton need a resolution on his future before the end of the season.
“We are still speaking with Clyney and his agent, but we have to know it in 10 days now,” Koeman said. “The club is doing and offering the maximum we can do, then we expect the decision of the player.
“I have spoken to Clyney. He is very happy. Maybe there is some interest, I don’t know because nobody has really had a bid for the player, but if I read the press then maybe there is some interest.”
Morgan Schneiderlin has also been linked with a move away from Southampton and Koeman admitted he faces a challenge to keep his best players at the club next season.
“All the players in the Southampton team are happy with how the team are doing but it is football, you never know,” he said.
“It is all about interest. We do everything to keep everybody in the team but it is difficult.”