The South Yorkshire club, currently bottom of the npower Championship, are looking to appoint their sixth manager in seven and a half years following the sacking last month of Keith Hill.
They received permission from Inverness to approach former England skipper Butcher, 54, on Monday and hope to meet with him this week to thrash out a deal that would see him swap the top two of the Scottish Premier League for a relegation scrap in English football's second tier.
Sean O'Driscoll, sacked by Nottingham Forest just hours after their Boxing Day win over Leeds, has turned down the chance of a speedy return to management at Oakwell after being offered the job following talks last week.
Barnsley director Don Rowing told Press Association Sport: "We've sought permission to speak with Terry Butcher and Inverness have agreed, so we expect to meet with him within the next 48 hours about the first-team manager's vacancy."
Butcher, in charge of Inverness since replacing Craig Brewster in January 2009, has guided them up to second place behind Celtic in the SPL table, while the club play Hearts in the semi-finals of the Scottish League Cup later this month.
Inverness have only lost against Motherwell and Celtic this season, are still in the William Hill Scottish Cup and are top scorers in the SPL so far with 44 goals.
The fact the former Coventry and Motherwell boss - Butcher also had brief stints as manager at Sunderland, Sydney FC and Brentford - has achieved this with a playing budget of £800,000 at the Tulloch Caledonian Stadium has not been lost on Barnsley, who operate on one of the tightest budgets in the Championship.
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."
- Sports & Recreation
- Scottish Premier League
- Terry Butcher