The 25-year-old's contract is due to expire at the end of the season and he has been heavily linked with a move to south Wales in recent days.
When quizzed on Cork's future on Friday, Koeman said that the player was "in Swansea".
"The club offered him a good contract but his feeling was not good to stay," added Koeman. "He wants to play more games and I can't guarantee that.
"It's up to the player, he finishes his contract this season.
"Every player is doing what they think is best for themselves and I don't have a problem with that."
However, Koeman stressed no deal would be completed in time for Cork to line up against Southampton in the Premier League on Sunday.
Cork's father, Alan, managed Swansea from October 1997 to June 1998.
Pep Guardiola issues a very blunt answer when quizzed by reporters on latest accusation levelled against Manchester City
'I think my opinion is more important than Roy Keane's. I know as a captain he does things sometimes with his arms, criticising his team-mates, but most of all it's a bit of frustration.' - Ruben Amorim hits back in Bruno Fernandes row
