The Polish goalkeeper, who has been strongly linked with a move to south west Wales in the past week, is said to be a target of the likes of Chelsea and Juventus and has been touted for a big money รยฃ3m move this summer.
It was thought that a bid had been tabled by Swansea for the Poland international last week, but todayรขโฌโขs Evening Post understand that a firm offer has yet to be made.
A spokeswoman for Jagiellona said that the club expected a bid from the Swans imminently, although what sort of price is to be offered is not yet known.
Swansea have upped the ante in their chase for a goalkeeping recruit after the loss of Dorus de Vries to Wolverhampton Wanderers yesterday, with just Yves Ma-Kalambay and David Cornell left on the books at the Liberty Stadium.
The club may be in the market for two new goalkeeping recruits over the summer if Ma-Kalambay doesnรขโฌโขt extend his contract beyond July 1st, when it is due to expire.