Lightning GM Steve Yzerman connected with Callahan's agent, Steve Bartlett, late last week and the two will touch base again this week.
It's unclear if Yzerman has already presented Bartlett with a formal offer for Callahan, who is coming off a three-year, $12.825 million contract.
During contract negotiations with the Rangers, prior to being traded, Callahan originally asked for an eight-year contract worth $7 million per season. While Callahan lowered his demands to a six-year deal worth $6.5 million, annually, the Rangers weren't reportedly willing to pay more than $6 million per season.
The Lightning has 16 players locked into contracts for the 2014-15 season, including defenseman Mattias Ohlund, who will not play due to a career-ending injury.
In addition to Ohlund's $3.6 million cap hit, the Bolts will have between roughly $20.37 million and $23.47 million in available cap space.
In 65 games with the Rangers and Lightning this season, Callahan registered 17 goals and 19 assists for 36 points.