Berra was released by League One side Wolverhampton Wanderers at the end of the season, and McCoist has admitted that he has already held talks with the 28-year-old.
The former striker told the Scottish Sun: "Christophe is someone that I'm looking at.
"I have spoken to him and to his agent. The signs are that we could possibly do something."
The former Hearts centre-back departed Molineux having made 141 league appearances since his arrival at the club in 2009.