Reports have linked the former England and Rangers defender with the Easter Road post vacated by Pat Fenlon on Friday.
But, after watching Inverness defeat Kilmarnock 2-1 in a soggy Highland capital, Butcher stressed that it was all rumour for now.
Caley Thistle climbed back to second in the Scottish Premiership with their win, and if there is interest from Hibernian in Butcher it is understandable, given the progress he has made at Inverness.
"All I would say is that it's just speculation as far as I'm concerned," Butcher said.
"We don't know how good this club could be, where it could go, or what's at the end for us.
"At this moment in time, I'm staying here - that's it."
He was more eager to discuss a seventh victory in 11 games for Inverness in the league this season.
"In the end it was a great win for us because we were put under a bit of pressure in the second half," Butcher said.
"Kilmarnock switched their system round and made it difficult for us. However, the boys saw it out very comfortably."
The loss to Inverness was Kilmarnock's first in three matches, but visiting manager Allan Johnston felt his side deserved to take home a point for their second-half efforts.
He said: "With the conditions in the first half it was difficult, but Inverness were probably the better team.
"However, I felt that we were by far the better team in the second half.
"We put them under a lot of pressure and were unlucky not to get the equaliser."
- Sports & Recreation