The 55-year-old was surprisingly sacked by Nottingham Forest a matter of hours after their Boxing Day win over Leeds, and had been the overwhelming favourite to replace Keith Hill at Oakwell. He met with Barnsley's board on Thursday but released a statement through the club ruling himself out of the running on Sunday night.
"Barnsley is a well-run club whose achievements in successfully maintaining their Championship status for so many seasons should never be underestimated," he said.
"But at this moment, and given the extremely disappointing and sudden nature of my departure from Nottingham Forest, I've respectfully declined the opportunity to become Barnsley's next manager. I wish the club, players and supporters all the best for the rest of the season."
Hill's former assistant, David Flitcroft, took Barnsley for their 1-0 FA Cup win over Burnley on Saturday.