A source close to the situation believes the two sides will be able to come to terms on an agreement prior to Wednesday's 3pm ET trade deadline.
If, though, a contract is not reached, the Rangers are expected to move Callahan.
Callahan was originally asking for a seven-year contract worth closer to $7 million per season. He came down to six-years and $6.75 million prior to the Olympic break, which the Rangers rejected.
Rangers GM Glen Sather and Callahan's agent Steve Bartlett are expected to resume discussions on Tuesday.