DETROIT -- The Detroit Tigers have designated reliever Jose Valverde for assignment, less than two months after bringing the veteran right-hander back to the major leagues for another chance to be the team's closer.

Valverde went 0-1 with a 5.59 ERA, converting nine saves in 12 chances. The Tigers will likely use Joaquin Benoit in most save situations for the time being.

Detroit has 10 days to make a move with the 35-year-old Valverde.

The Tigers recalled right-hander Al Alburquerque from Triple-A Toledo to replace Valverde in the bullpen. They also put outfielder Matt Tuiasosopo on the disabled list with a strained left intercostal and recalled outfielder Avisail Garcia from Toledo.

Detroit general manager Dave Dombrowski said he'd like Valverde to go to the minor leagues to work through his struggles.

"We have asked him if he would go to Triple-A for us, and try to work with him there, try to get him straightened out," Dombrowski said. "He did not give us an answer on that. It really doesn't make a difference at this point, since we would still have to get waivers at some time. He was open-minded to it. He didn't say no to it, but he needed some time."

Valverde faltered during the 2012 postseason, and the Tigers were prepared to let him leave via free agency, but he didn't sign anywhere else, and Detroit eventually brought him back on a minor league deal.

He was called up to the majors toward the end of April.

Benoit is 1-0 with a 1.80 ERA and four saves, and Drew Smyly has also pitched well out of the bullpen. Manager Jim Leyland said he'd like Valverde to stay in the organization but can respect whatever decision he makes.

At least for now, Benoit will have a chance to close games.

"Benoit, when available, healthy and ready to go and rested, will get most of the closing opportunities," Leyland said. "And anything else, we'll mix and match."