The Tykes made their move for former England international Butcher after being rejected by Sean O’Driscoll.
Barnsley, who sacked Keith Hill at the end of December, are currently bottom of the Championship.
Butcher has not managed in England since December 2007 when he left Brentford by mutual consent following a run of 23 matches with just five wins.
Caley Thistle have been the SPL’s surprise package this season and they currently sit in second position in the table, a standing that would see them qualify for the Champions league qualifying stage if they were still there at the end of the season.
Butcher’s team are unbeaten in their last nine games in all competitions and have lost only three league games all season, one fewer than league leaders and Old Firm giants Celtic.