Inverness Caledonian Thistle have granted the former England captain the opportunity to discuss the vacancy at Easter Road but are hopeful of convincing him to stay
The 54-year-old has guided his side to seven wins in the Scottish Premiership this season and is seen by Hibs as the right man to replace Pat Fenlon, who left Easter Road following their Scottish Cup exit to Hearts.
Butcher was linked with the job on Monday but Inverness insisted that they had not received an official approach for their man, though have now confirmed that the former England captain is free to talk to his suitors.
"Terry has been informed of the situation and has expressed an interest in meeting with Hibs officials," chairman Kenny Cameron told the club's official website.
"The club has, with great reluctance, granted him permission to do so. We will, however, continue to do everything possible to ensure that Terry remains our manager.
"Given our current position in the SPFL and the fact that once again we have a cup semi-final to look forward to, it is inevitable that, if any managerial positions arise, our manager will be on the wanted list.
"We have a game on Saturday and it's important that our club's focus is on taking three points to maintain our challenge at the top of the league.
"As with the Barnsley approach in January, we will be making no further comment until we're fully aware of the outcome of discussions."