Fellow southpaw Brett Cecil, who will be entering Spring Training as a reliever for the first time in his career, is one player who figures to benefit if Oliver is out of the mix.
"Obviously it would help me out a little bit if he did retire, but I would rather him back on the team, to be honest," Cecil said at the Blue Jays Winter Tour, presented by TD, stop at Rogers Centre on Saturday.
Oliver was an important fixture in Toronto's bullpen last season, tying for the team lead in appearances with 62, while his 10 1/3 innings pitched in high-leverage situations was second most among Blue Jays relievers, according to FanGraphs.com. The 42-year-old was leaned on heavily in a year he posted a career-best 2.06 ERA.
Replacing Oliver's production won't be easy, but Cecil has been equally effective against lefties over the last three seasons, holding left-handed hitters to a .208/.270/.300 batting line, while Oliver has posted a .220/.272/.314 mark. Cecil's numbers against lefties during that span, over a smaller sample than league qualifiers, is among the best in baseball.
The 26-year-old Cecil has been homer-prone throughout his career, but he has a good chance to minimize the long ball by not having to go through lineups multiple times. He didn't allow a home run over his 11 innings of relief work last season and has surrendered just four to left-handers over 337 at-bats since 2010.
After struggling in past stints as a starter, particularly against righties, Cecil could shine as a left-handed specialist, with theoretically more zip on his stuff.
Cecil enjoyed an uptick in velocity following his switch to the bullpen, with his average four-seam fastball spiking from less than 90 mph as a starter to 92 mph over his 12 appearances as a reliever, according to brooksbaseball.net.
"Right now, I feel like the bullpen is that place for me where I can succeed," said Cecil, whose past experiences as a reliever include closing at the University of Maryland. "In college, I had that mentality of going out and blowing it out for one inning, two hitters, one hitter.
"It seems like a better suit for me right now."
Cecil doesn't want to turn the page on starting, but he understands a move to the bullpen could have a positive impact on his career, especially on a Blue Jays team without any vacant rotation spots.
"I would prefer to be in the starting rotation, but in the end, I want to do whatever makes the team successful and whatever makes me successful," Cecil said.
Cecil appears to be a lock to break camp with Toronto based on his track record versus left-handers and the fact he's out of options, which means he would have to clear waivers in order to be sent to the Minors.
Lefty Aaron Loup, who will be competing with Cecil after an impressive rookie campaign, may begin the season at Triple-A Buffalo, but he also stands to benefit in the event Oliver does not return.
Loup held left-handed hitters to a .207/.220/.241 batting line, while holding righties to a .638 OPS.
"It's definitely going to help me out being here last year," said Loup, who posted a 2.64 ERA over 30 2/3 innings. "You kind of know going in that's what I'm going to be doing, is facing lefties. That doesn't mean I can't get right-handers out."
The Blue Jays will have one more lefty in the bullpen in J.A. Happ, who is likely to serve as a long reliever. Right-handers Casey Janssen, Steve Delabar, Brad Lincoln, Esmil Rogers and Sergio Santos, who appeared in just six games last season and is coming off shoulder surgery, are the leading candidates to fill out the remaining spots.
Hard-throwing righty Jeremy Jeffress, who's also out of options, has the potential to emerge in the event of an injury or something performance related.
An Oliver departure would make some decisions easier for Toronto -- especially with Cecil and Rogers being out of options -- but it doesn't settle every job for a Blue Jays bullpen that will look entirely different from the one assembled in Dunedin, Fla., last Spring Training.
Chris Toman is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.