Bishop had a 2.54 goals-against average and .910 save percentage in 39 games this past season, split with the Kings and Tampa Bay Lightning.
He is a two-time Vezina finalist with a career .919 save percentage in 270 appearances.
“Ben has proven that he is one of the elite goaltenders in the NHL,” said Stars general manager Jim Nill in a release. “This offers us the opportunity to negotiate with him before the free agency period begins.”
The Stars sent a fourth-round pick in 2017, originally belonging to the Montreal Canadiens, to the Kings in exchange for Bishop's rights.
Dallas has until July 1 to reach an agreement with Bishop, before he'll be able to negotiate with all 30 other teams as a free agent.
The team missed the post-season this year after posting the worst team save percentage (.893) in the league. The Stars were coming off a season in which they posted the second-best record in the NHL.