"There is still an offer on the table from ourselves, which we still hope Leon will accept," Swans chairman Huw Jenkins told the Wigan Evening Post.
"But we won't be putting a time-scale on it, because Leon has been a great servant to this football club. Whenever he sees fit to make a decision, the door will always open for him.
"I don't know exactly what his plans are, but we went along with his wishes to exercise his right to become a free agent this summer.
"Whatever he wants to do, whatever choice he makes, we are fully behind him because his service to us has been so fantastic."