Marleau, a Group II restricted free agent, was tied for fourth on the team with 21 goals and tied for second with five game-winning tallies. He also had 23 assists in 79 games.
The 22-year-old Marleau also matched Owen Nolan's team-record six-game goal streak from March 30-April 10. He led the Sharks with six goals and 11 points in 12 playoff games.
Sturm, 23, also a Group II restricted free agent, posted career highs with 21 goals and 41 points in 77 games last season. He also played for Germany in the Olympics, and had one assist in five games.
Heins, a Group VI unrestricted free agent, had two assists in 17 games last season.
San Jose has five unrestricted free agents: Mike Craig, Theo Fleury, Stephane Matteau, Teemu Selanne, and Gary Suter. Fleury's rights were acquired from the New York Rangers late last month for a sixth-round draft pick, and Selanne became an unrestricted free agent Monday after he declined the Sharks' latest contract offer. The club deemed his counter-proposal to be too steep.
The Sharks are not optimistic about re-signing Selanne.
"History is not with us," General Manager Dean Lombardi told the San Jose Mercury News. "They (Selanne and his agent, Don Baizley) still left it open, but it doesn't ever seem to work out that way. There were no bad feelings, but he felt like he wanted to see what else was out there."