Soria, with damage to the ulnar collateral ligament in his right elbow, was in Los Angeles on Tuesday to confer with specialist Dr. Lewis Yocum.
Crow's role? Yost was non-committal.
"Bullpen guy," Yost said. "He made the All-Star team, it's a great fit."
Greg Holland and Jonathan Broxton are the top two candidates to replace Soria in the closer's role, although Crow could figure in that picture as well.
"He's got the stuff to do it," Yost said. "We're just trying to put together a darn good bullpen."
Removing Crow from the starting candidates narrows the field to seven, Yost said. That leaves Felipe Paulino, Luis Mendoza, Danny Duffy and Everett Teaford competing for the final two spots behind Luke Hochevar, Bruce Chen and Jonathan Sanchez.
Duffy seems to have taken the lead among the battling foursome with the other spot narrowed to Paulino and Mendoza. Teaford has doggedly stayed in the hunt as well.
That eliminates Vin Mazzaro and Sean O'Sullivan, two right-handers with big league starting experience, from the rotation race.
Yost did not rule out the possibility that Crow could be used as a starter during the season.
"We think that Crow has an opportunity to be a really good starter for us, but right now the best makeup of our team is with him in the 'pen," Yost said.
Crow had no argument with the decision.
"I don't really care either way," Crow said. "We've got so many starters pitching so well, so I'll just go out there and try to repeat what I did last year. ... I think the bullpen is going to be one of the strengths again this year."
Of the top three starters, Hochevar has the cleanest record with a 2.25 ERA in three Cactus League games. He's given up two runs in eight innings with seven strikeouts and just one walk.
Chen has struggled in two of his three starts and has an 11.74 ERA, giving up 10 earned runs in 7 2/3 innings of three Cactus starts. He'll start on Thursday in a split-squad game against the Chicago White Sox.
"I want to see him pick it up a little bit, but he's doing fine. He's getting his work in. Bruce is going to be Bruce," Yost said. "Once we get past the off-day [which was Monday], I expect guys to start their minds focused toward that first start and really picking it up. Like Sanchez and Teaford did [Monday]; both of them did pretty good."
Sanchez and Teaford each pitched four scoreless innings in Minor League games against Texas Rangers farmhands on Monday.
Coming off an injury-shortened season last year with the San Francisco Giants, Sanchez got a late start, and in two Cactus games has given up seven runs in three innings for a giant-sized 21.00 ERA. But he gets a pass because of the injuries, and his stuff looked very good in his Minor League outing.
Teaford, who could start or relieve, hasn't permitted a run in five Cactus League innings. Mendoza has been especially impressive with a 0.84 ERA in three starts and 11 strikeouts, one walk in 10 2/3 innings.
Duffy had a sensational first outing with five strikeouts in two perfect innings against the Cincinnati Reds, then gave up two runs in three innings against the Los Angeles Dodgers. He'll make his third start in Thursday's split-squad game against the Angels.
Paulino had what he termed his best outing on Tuesday, giving up one run in four innings in a 6-4 victory over the Angels. In three games, he's given up five runs in nine innings.