The former St Johnstone forward, midfielders Kevin Thomson and Tom Taiwo, as well as defender Tim Clancy, have been informed by Butcher that they are free to leave.
Although Vine has been told by the former Inverness Caledonian Thistle manager that he will struggle to break into the team, the 31-year-old is still waiting for confirmation over his future at Easter Road. Vine, though, admitted he would not be surprised if the club said he was allowed to find new employers this month.
The forward - signed by Pat Fenlon last summer - has only made six competitive starts in a total of 13 appearances this season. Since Butcher arrived in November, however, the closest Vine has come to game time was as an unused substitute outing in the Scottish Cup win at Ross County that month.
"It does not take a rocket scientist to work out that I have not featured since the manager came in," admitted Vine. "Reading between the lines, it will probably be the case that the club will tell me I'm free to go.
"I have had one conversation with the manager and he told me it would be difficult to get game time because he is obviously going with other people at the moment.
"There are not many times that I've been at a football club and not been involved. The minute it's happened at any other clubs, I've tried to get myself away. If I'm not on the pitch and not in the squad, it does not matter if I'm 19 or 31, it means I've got to go and play football.
"The only time I've sat and finished a contract is at QPR off the back of injuries and a lot of things happening. I've maybe gone on loan ten times so that's my attitude; if I am not playing then I have to get out.
"It does not matter what age you are, you want to play. I want to play this Saturday, next Saturday, last Saturday - that's the way I am. If it's the best thing for me to get out and play football, I'll be trying to do that."
Vine - who counts Hibs as his 12th professional club - is an experienced enough campaigner to not get too down about his predicament.
"There are no hard feelings about it," he said. "The game is about opinions although I'm disappointed that I have not been given a chance under the new manager.
"I think I have started four league games, which is disappointing for me because I have not really settled or hit the ground running.
"I am my own biggest critic, I struggled a bit and then the team were struggling a bit. I am really disappointed I have not had a chance so far but that does not change the fact that I work hard.
"At my age you do start assessing the situation. If it is going to go the way that I can leave, then I have to do what's best for me, whether that's staying up here, going back to England or anywhere. At this point in my career, every option is going to be looked at."
Like Vine, Thomson, Taiwo and Clancy are also in the final six months of their deals.
Thomson, the former Rangers playmaker, and his fellow midfielder Taiwo have each made only two substitute appearances under Butcher, while fit-again defender Clancy is wanted by Northern Irish side Derry City and appears likely to join the club at some time in the coming weeks.