Caley Thistle confirmed 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.
Chairman Kenny Cameron added: "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.
The former Rangers and England captain turned down a move to Barnsley in January and Cameron hopes he remains loyal to Inverness.
Cameron, whose club face Hibs at Easter Road on Saturday, 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."
A statement on the Hibernian website confirmed that they have been given the green light to speak to Butcher, and it was also announced that Jimmy Nicholl will oversee first-team affairs for Saturday's clash with Inverness.
The statement read: "Hibernian FC confirmed that following an approach, chairman to chairman in the appropriate manner, permission has been received to speak to Terry Butcher regarding the vacant managerial position at the club.
"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."