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."
Cork's father, Alan, managed Swansea from October 1997 to June 1998.
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