The Habs are currently evaluating their options, as they are up against the salary cap and are also scouring the trade market for a top-six forward and a top-four defenseman.
It's believed Jagr is looking for a one-year contract.
Canadiens GM Marc Bergevin spoke with Jagr's agent, Petr Svoboda, on Friday and the two sides briefly connected today.
Jagr could receive a base salary in the $1.5 million to $2 million range, with performance bonuses that could see his cap hit come in around $4 million.
In 45 games with the Dallas Stars and Boston Bruins this past season, Jagr registered 16 goals and 19 assists for 35 points.
The native of Kladno, Czech Republic, has played in 1,391 career NHL regular-season games with the Pittsburgh Penguins, Washington Capitals, New York Rangers, Philadelphia Flyers, Stars and Bruins, and has accumulated 681 goals and 1,007 assists for 1,688 points, along with a plus-278 rating and 959 penalty minutes.
Jagr was drafted fifth-overall by the Penguins in the 1990 NHL Entry Draft.