Callahan is looking for a seven-year contract worth between $6 million and $7 million per season, while Girardi is looking for a deal in the five-to-seven year range.
If the Rangers are unable to sign either player by the March 5 trade deadline, they are expected to trade them.
The Olympic trade freeze lifts tonight at midnight, but the Rangers aren't expected to make a move involving Callahan or Girardi just yet.
"(The Rangers) don't have anything imminent in terms of trade for either guy. Expect it all to play out over 7 to 10 days," McKenzie tweeted.
The Anaheim Ducks, Boston Bruins and Detroit Red Wings are among the teams interested in Girardi, who is looking for a deal worth more than $5 million, per year, on his next contract.
Callahan has caught the attention of the St. Louis Blues and Vancouver Canucks, among others.