The move would give Boston one of the NHL's all-time great scorers as it tries for its second Stanley Cup in three seasons. Jagr has 1,679 points in 1,380 games with Pittsburgh, Washington, New York Rangers, Philadelphia and Dallas.
He won the Hart Trophy as league MVP in the 1998-99 season and is a five-time winner of the Art Ross Trophy as league scoring champion.
He has plenty of playoff experience, and was a key part of Pittsburgh's Stanley Cup wins in 1991 and 1992. He also helped the Czech Republic win the gold medal at the 1998 Nagano Olympics.
He remains a productive forward at age 41, putting up 14 goals and 12 assists in 34 games with Dallas this season.
The Stars have been one of the biggest sellers leading up to Wednesday's trade deadline. They have traded former captain Brenden Morrow to Pittsburgh and have reportedly moved forward Derek Roy to Vancouver.
Reports say the Stars will get two prospects and a draft pick in return.