With Clyne's contract set to expire in 2016, Southampton know failure to tie him to a new contract will leave them at risk of losing him for nothing. Alternatively, they may be forced to accept a reduced fee for him this summer or next January.
That is why Koeman is keen to get Saints officials and Clyne's representatives in the same room. If Clyne refuses to agree a new deal then Southampton can start negotiating with interested parties as soon as possible. However, Koeman has revealed that the club have yet to receive any serious offers.
"We don't have really a serious bid"
"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 reporters.
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"I hope [he will stay], but I can understand if there is any interest from other clubs.
"We don't have really a serious bid.
"Normally the left-back position is more difficult to find good players"
Interestingly, it seems Koeman is preparing for the worst, suggesting that he would not find it too difficult to find a replacement if Clyne does decide to leave. He does, however, admit that few players have as much experience as Clyne, 23, at the same age.
He continued: "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."
Louis van Gaal seems most interested in signing the England international with Rafael looking as good as gone. The Brazilian has failed to impress at Old Trafford this season and it is reported that Manchester United will listen to offers for him this summer.
That would leave a first-team place open for Clyne, who could also link up with former team-mate Luke Shaw. However, Chelsea and Liverpool are likely to follow it up with tempting offers.
Chelsea would not be able to guarantee first-team football with Branislav Ivanovic ruling the roost at Stamford Bridge, but Liverpool will be able to offer him a key role if and when Glen Johnson departs.
It will come down to whoever has Champions League football. If Manchester United miss out to Liverpool it automatically becomes much harder to convince players like Clyne to join. Money may talk, but the chance to play in Europe's top tier competition should be a deciding factor for the 23-year-old.
Do you think Nathaniel Clyne should stay at Southampton or go to Liverpool, Chelsea or Manchester United? Give us your views in the comments box below!