Designated hitter Ken Griffey Jr. and Russell Branyan, believed to be the most likely to return to Seattle next season, have not yet filed for free agency.
The Mariners are not expected to discuss offers with either Batista or Chavez.
The 38-year-old Batista posted a 7-4 record and 4.04 ERA for the Mariners during the final year of his three-year, $27 million contract. He appeared in 56 games, all in relief. The veteran right-hander won 16 games for Seattle in 2007 but slumped to a 4-14 mark in '08.
Chavez, one of the players acquired in the blockbuster 12-player, three-team trade with the Mets and Indians at the Winter Meetings last year, had his season cut short by a devastating knee injury on June 19 in a collision with then-shortstop Yuniesky Betancourt.
He started the season in the leadoff spot because a bleeding ulcer put Ichiro Suzuki on the disabled list for the first time in his career. Chavez began the campaign with a 10-game hitting streak.
Chavez was batting .273 with nine stolen bases in 10 attempts at the time of his season-ending injury.
Bedard's second season with the Mariners ended the same way as his first -- in surgery.
He had season-ending surgery on his left shoulder on August 14. Bedard posted a 5-2 record and 2.82 ERA in 15 starts, which could lure the Mariners into trying to work out a one-year deal worth less than the $7.75 million he received last season.
Sweeney said earlier on Friday that he planned on playing in 2010 and would like to return to the Mariners.
"My body feels great and I have the blessing of my wife to continue playing," Sweeney said. "Last year was the most fun I've ever had and it would be great to come back."
Sweeney batted .281, hit eight home runs and drove in 34 runs while splitting the designated hitter duties with Griffey.
"If Oct. 4 was my last game in a Mariners uniform, it will be an unforgettable day," he said. "To watch Felix win his 19th game, [David] Aardsma get his 35th save, Junior to get a hit in his last at-bat, and to be a part of the celebration on the field after the game was special."
The 36-year-old said he has not heard from Mariners club officials since the end of the season.
"If they decide to go in another direction, I could understand it," he said.