Callahan, 28, is looking for a seven-year contract worth between $6 million and $7 million per season.
His agent, Steve Bartlett, who is heading to Sochi next week to attend the Winter Olympics, told TFP he is open to continuing negotiations throughout the break in the NHL schedule, though nothing new is officially scheduled, as of now.
Bartlett spoke with Rangers GM Glen Sather Wednesday and Thursday, but the two sides were unable to come to terms on an agreement.
Girardi, 29, is in the same boat as his teammate. Contract negotiations on his end have calmed.
It's believed Girardi is seeking a five-year contract worth more than $5 million, per season.
Teams are allowed to re-sign their own players during the Olympic break, but cannot begin trading them until Feb. 24.
If Callahan and Girardi go unsigned past the Olympics, the odds of them being moved will increase significantly.