Sky Sports understands Switzerland striker Innocent Emeghara has set his sights on a move to England.
Wilfried Zaha wants to use his season back at Crystal Palace to relaunch his Manchester United career.
Cywka's current deal expires this summer and the Tykes were keen to tie down the Pole to a new contract.
However, both parties have failed to agree terms and the 25-year-old seems set to leave on a free transfer.
The news is sure to alert a host of clubs to the availability of the former Wigan and Derby man.
Cywka made 52 appearances and scored eight goals during his two-year spell at Barnsley.