Those four now have five days to negotiate exclusively with the Mariners, as all Major League clubs have a five-day window to deal with their own free agents. Players will be able to sign contracts with new clubs beginning Wednesday at 9:01 p.m. PT.
Bard, Wright, Kennedy and Pena all made the Mariners' roster last year after originally signing as Minor League free agents. Pena joined the club in late July, while the other three were with the team from Spring Training.
All four could potentially be brought back on similar deals, with Wright seeming the most likely to draw a Major League offer after becoming a key piece of the bullpen. The 36-year-old went 2-3 with a 3.16 ERA in 68 1/3 innings.
His 60 relief appearances were second only to the 65 of closer Brandon League, in a young bullpen that employed five rookies over the course of the season.
Wright, who turns 37 on Dec. 24, has only been a reliever the past four years after spending the first 12 years of his career primarily as a starter.
"I feel like with each year I've thrown out of the bullpen, I'm getting better," Wright told MLB.com on the final day of the regular season. "I finished up strong, felt strong, felt healthy to go out and take the ball every day.
"I've got to figure I'm probably a valuable piece for somebody out there. I'll keep doing what I'm doing and get ready for Spring Training, no matter who it's with. I'd love it for to be here, but I know how it is. After the season is over and nobody is on the disabled list, it looks like we've got a whole bunch of guys. But when it comes to crunch time and you need guys to be out there to produce and be durable, I'm usually one of those guys. So we'll see."
Wright said that he enjoyed being part of a youthful group in the bullpen, acing as the one established veteran alongside League. The only downside, he said with a grin, was the expense of outfitting all the newcomers with backpacks to wear out to the bullpen to signify their rookie status.
"We spent like two grand on freaking backpacks this year," he said. "We had a different one almost every month. It was fun though. You're thinking you've got [Josh] Lueke and [Dan] Cortes that you're going to be relying heavily on, and then all the sudden [Tom] Wilhelmsen and [Steve] Delabar come in with good arms.
"They've just got to learn how to go about their business and be ready to go every day. That's what Brandon and I were for -- to help them learn that, and they did a good job. I think I was a big part of that, and it's something I'm happy to do. I don't think a lot of guys are all that excited about being the old babysitter type, but I've got three kids of my own and I'm kind of used to it."
Kennedy, 35, also filled a valuable veteran role throughout the year, though his offensive production dipped dramatically in the second half and he lost most of his playing time to youngsters down the stretch.
Kennedy was one of the team's top hitters early in the season, batting .259 with six home runs and 30 RBIs in the first half. But he hit just .190 with one home run and eight RBIs after the All-Star break, as Dustin Ackley took over at second base and Kyle Seager and Alex Liddi eventually earned most of the playing time at third base.
Bard, 33, has spent parts of the past two seasons with Seattle as a non-roster invitee. He was called up from Tacoma for the final three months this past year and hit .210 with two home runs and 11 RBIs in 26 games.
Pena, 29, signed with the club on July 27 after being released by the D-backs. He hit .209 with two home runs and eight RBIs in 22 games.
With those four becoming free agents, the Mariners' 40-man roster now stands at 36. That allows flexibility to add players off the 60-man disabled list, which Seattle must do by Wednesday in order to retain control. The Mariners have three players on the 60-day DL: outfielder Franklin Gutierrez, closer David Aardsma and catcher Adam Moore.