The English international, 23, has been one of the Saints' most impressive performers this season, and, with his contract set to expire in 2016, he's been linked with moves to some of the Premier League's largest clubs - Manchester United and Chelsea being the most noteworthy.
But Koeman, who notes that an official bid has not been submitted by anyone for Clyne's services, says the club will begin the process of working on a new contract with the defender this week.
"The contact is between Les Reed [Southampton's executive director] and the agent and Clyne, but I think after Wednesday it's a good time to talk about that - of course, we like to know what his decision is about the future," Koeman told the Daily Telegraph.
"I hope, but I can understand if there is any interest from other clubs," Koeman said when asked if Clyne will remain with the club for the foreseeable future. "We don't have really a serious bid. It's not I think the most difficult position.
"Normally the left-back position is more difficult to find good players. But, even the right full-back position, there are not a lot who have played on the level as Clyne has been doing this season."
He's not wrong.
Among those who have made at least 15 appearances this season, Clyne leads the team with 3.7 tackles per 90 minutes, while his 1.4 successful dribbles are good for fifth. It's an impressive ranking for a right-back, and one that highlights his importance to the Saints' attack on a team that boasts quality dribblers like Dusan Tadic, Sadio Mane and Eljero Elia.