Barnsley sacked Keith Hill at the end of last month after they slipped to the bottom of the table and were hoping to appoint Sean O'Driscoll as his permanent replacement.
But O'Driscoll, 55, surprisingly sacked by Nottingham Forest just hours after their Boxing Day win over Leeds, turned down the Barnsley job on Sunday and club director Don Rowing said on Monday morning that interviews would resume at Oakwell in the next 48 hours.
Inverness chairman Kenny Cameron said in a statement: "We have given Barnsley FC permission to speak to Terry.
"Given our current position in the SPL and the fact we have a cup semi-final on the horizon, it is inevitable that if any managerial positions come up our management team will no doubt be on the radar.
"We will be doing everything possible to ensure that Terry remains with the club and finishes what has been an incredible journey to date for us all."
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