But Caley Thistle have vowed to do everything possible to hold on to the former England captain.
Caley Thistle confirmed on Tuesday afternoon they had received an official approach from their Scottish Premiership rivals, who have been looking for a new manager since Pat Fenlon quit on Friday, and accepted Butcher's desire to speak to Hibs chairman Rod Petrie.
But they hope he remains loyal to the club as he did in January when he rejected an offer to take over at Championship club Barnsley.
Inverness chairman Kenny Cameron said: "Terry has been informed of the situation and has expressed an interest in meeting with Hibs officials. 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."
Butcher last week led Caley Thistle to their second League Cup semi-final against Hearts in two seasons and they sit third in the league, three places above Hibs.
Cameron said: "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."
Hibs insisted their approach had been made in the correct manner.
A club statement added: "Hibernian FC is grateful to Inverness CT FC for granting permission.
"Both clubs have an important league match on Saturday with three vital points at stake.
"Chairman Rod Petrie met Jimmy Nicholl at the Hibernian Training Centre this morning and confirmed that Jimmy and the backroom staff should prepare the team this week and take the match on Saturday."
- Sports & Recreation
- Caley Thistle
- Jimmy Nicholl