Koeman: Contract extension on the cards for Forster
Forster has helped kick-start Southampton's season since returning from a long-term knee injury in January, with the England keeper also making a comeback to the international scene.
The 28-year-old - out of contract in 2018 after joining from Celtic two years ago - and his performance will not have gone unnoticed by the Premier League's bigger clubs, reportedly Chelsea.
When asked if a contract extension was on the cards for Forster, Koeman said: "That's a possibility, yes."
Koeman, whose Southampton are seventh ahead of Saturday's hosting of Newcastle United, added: "We will try to hold onto everyone of course.
"But we know our situation and we know we can't win against the big teams with a lot of money.
"That's a good thing that our players have ambition, everybody wants to play at the highest level.
"But we will do everything we can to keep the players in."