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 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."
- Sports & Recreation
- Clydesdale Bank Premier League
- Andrew Shinnie
- Caley Thistle