If they cannot, the Post suggests the Rangers trade both of them for draft picks and prospects before the Mar. 5 trade deadline, instead of risking them both leaving as unrestricted free agents in the summer.
Callahan and Girardi are the team's most prized impending free agents, with defenseman Anton Stralman and forward Brian Boyle also in need of new deals.
The Rangers currently sit second-last in the Metropolitan division, but are only six points behind a playoff wildcard spot, currently owned by the Toronto Maple Leafs.
Callahan's annual salary cap hit on his current deal is $4.275 million, while Girardi's is $3.325 million.
Both players will receive significant raises on their next contracts, but could likely cash in more on the open market, something the Rangers are aware of.
Rangers GM Glen Sather has time before he makes any decisions, and the team's performance over the next several weeks will determine which route he plans on taking.
Contract talks between the Rangers and the agents for Callahan and Girardi should pick up in the New Year.