Mujica, who was an All-Star with St. Louis in 2013, went 2-4 with a 3.90 ERA and eight saves in his first season with Boston in 2014.
Ogando has been a free agent since being non-tendered by the Rangers in December. Ogando made just 27 relief appearances in 2014 due to an elbow injury. He went 2-3 with a 6.84 ERA.
Ogando, who was an All-Star in 2011, also has experience starting at the major-league level, going 19-12 with a 3.40 ERA in 48 career starts.
Street converted 41 of 44 save opportunities last year, going 2-2 with a 1.37 ERA.
Rangers general manager Jon Daniels said Tuesday Ranaudo is in play to become the No. 5 starter in the rotation, but if he doesn't win the job, he will likely start in the minors.
Ranaudo posted a 4-3 record with a 4.81 ERA in 2014 for Boston in 39 1/3 innings pitched. Ross went 3-6 with a 6.20 ERA in 78 1/3 innings for the Rangers.
However, McClendon hasn't totally given up on the idea of Wilhelmsen potentially transitioning to a starting role down the road, per MLB.com.
"I don't think it's totally dead," McClendon said. "I would say it's probably a long shot. My plan, as we speak right now, is to maybe stretch him out in spring and just play with it a little bit and see what happens, but I think it's a long shot. He was just so good in the role he was in, it'd be hard to take him out of that role."
Wilhelmsen pitched multiple innings in 24 of his 57 appearances last year. The former closer went 3-2 with a 2.27 ERA and 72 strikeouts in 79 1/3 innings.
"I really tried not to change anything at all, [other than] try to simplify a little bit," Wilhelmsen said. "If I was going in in the fourth inning, I knew I'd have to throw two or three innings and I just really attacked the zone. But it's not like you don't attack the zone any other time. It's the same thing. You have to get outs."
Perkins missed the last two weeks of the regular season due to a forearm injury, but said that's no longer a problem. He took two weeks off once the season concluded, and went for a precautionary MRI just to make sure the injury wasn't serious. "I took two weeks off and started doing shoulder stuff as part of the rehab to strengthen it and everything went well," Perkins said. "I started throwing again in mid-December. The way I've been able to ramp up throwing, everything has been good."
The 31-year-old Perkins posted a 3.65 ERA over 61 2/3 innings last season.
Alburquerque originally filed for $2.05 million in arbitration while Detroit offered $1.375 million, according to Heyman. The team made the deal official Sunday, avoiding arbitration.
The five-year veteran went 3-1 in 2014 with a 2.51 ERA in 72 games.
In 2014, Duensing went 3-3 with a 3.31 ERA.