Brynjar Gunnarsson is training with the Reds. Gunnarsson is out of contract following a four-year spell with Stoke City.
Gunnarsson training with Barnsley
The 27-year-old has been capped 34 times for Iceland and made 128 league starts for the Potters. He was signed from Orgryte for £600,000 in 1999 and can play in defence or centre midfield.
Thordarson told the official Barnsley website: "Brynjar will come and train with us."