The 28-year-old is travelling from Warsaw, where he has been with the Poland national side, for a medical, with a view to signing a three-year contract with Burnley.
The deal had looked dead, with Burnley moving on to other targets after failing to strike an agreement with his club, who wanted €8m, with the Clarets offering €6m.
But the Clarets have gone back in for the pacy wideman, and will now look to complete a deal before 11 p.m.