AFC Bournemouth have signed Christian Atsu from Chelsea on a season-long loan deal.
Midfielder Miguel Pallardo has signed a new one-year deal with newly-promoted Hearts while Danny Wilson leaves.
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.