Portsmouth have named Richie Barker as their new manager and Steve Coppell as director of football.
Wigan have announced Uwe Rosler as their new manager after agreeing compensation with Brentford.
The likes of Andrew Shinnie and Billy McKay, who have 29 goals between them this season, are believed to be attracting interest from other clubs.
Shinnie struck Caley Thistle's first equaliser in a 2-2 draw with St Mirren on Boxing Day from 25 yards, which kept them second in the Clydesdale Bank Premier League, and is mulling over a contract offer that would keep him at the club beyond the end of the season.
Butcher said: "People talk about the January transfer window and people being interested in our players.
"At the start of the season if you had said clubs were interested in our players then you would have said we must be doing pretty well.
"You can't have it both ways where you are doing very, very well and there is no interest in your players. That just doesn't happen.
"Let them admire my players from afar. Let's get through January and at the end of January there is a semi-final.
"Let's get through January and into a cup final and a cup tie against Killie to look forward to."
While Inverness have the Scottish Communities League Cup clash against Hearts and William Hill Scottish Cup trip to Rugby Park to look forward to, there are more pressing matters with games against St Johnstone and Ross County to come before the SPL winter break.
Butcher's men have only lost to Celtic and Motherwell this term, although they had the woodwork to thank yesterday with Lewis Guys twice striking the frame of the goal and seeing two goals disallowed.
Dougie Imrie and Steven Thompson both put Saints ahead only for Shinnie and Richie Foran to level.
Butcher said: "Going forward, we were sensational at times.
"It was more like a basketball match or a table tennis match when the ball is fizzed from one end to the other.
"It was really exciting. We generally don't like open games as managers because you want to keep it tight and be in control.
"But I thought we were in control when it got to 2-2 but we just couldn't get the goal."
St Mirren manager Danny Lennon had to contend with suspensions to Jim Goodwin and Marc McAusland plus several injuries, but was disappointed not to snatch a win.
"They are a terrific group to work with, although after getting off to a very good start perhaps we didn't show our true qualities in terms of our ball retention in the first half," he said.
"But we were always dangerous on the break.
"Then in the second half we dictated the game and it's a very valuable point against a team who are flying high and that's pleasing, although it could just as easily have been three in terms of the opportunities we had."