DETROIT — If the Tigers could pick up a hardened veteran reliever, a guy who has more than 100 career saves, and held right-handed hitters to a .197 average as recently as last year, and could do so for next to no cost, they should right?

No-brainer. The Tigers have been actively looking for a guy like that to add to what’s been a beleaguered bullpen all season.

Well, they might have a chance to do so ... considering the guy is named Octavio Dotel.

For the first time in a long time, the reports on Dotel — who has been out since April 20 with elbow inflammation — are positive.

He’s throwing off the mound, feeling good, according to Tigers manager Jim Leyland.

“You never know how this works. It might turn out to be a helluva trade at the deadline. I don’t know. I have no idea,” Leyland said. “If he could come back like the Dotel of the second half of last year, it would be a nice trade at the deadline that you didn’t have to make.

“But I can’t predict that. I’m not saying that’s going to happen, because I don’t know that.”

Dotel went 5-3 for the Tigers (and 3-1 in the second half) last season, posting a 3.57 ERA and a WHIP of 1.069 in 58 innings, allowing just 17 percent of inherited runners to score, and recording 11 holds.

After re-signing with the Tigers on a one-year, $3.5 million deal, Dotel appeared in just six games early this season, before being shut down with a sore elbow. For most of the time since then, he’s been in Florida, trying to rehabilitate his 39-year-old arm.

At one point, Leyland even said “I think he’s trying to see if he still has it.”

Apparently, the desire is still there, at least enough for Dotel to continue working at it, to see if he can come back this season.

“He’s a proud guy, a veteran guy. He’s been around a long time. He’s doing everything he can. That’s not easy to sit down there in Lakeland, Fla., all summer long, rehab. That’s a tough ticket. I give him a lot of credit. A guy that’s played as long as he has. He could’ve just said, ‘You know what? I’ve had enough.’ He wants to help us. And I really appreciate that,” Leyland said.

“It sounds like it’s very encouraging. But I don’t count on them until they’re here, pitching for us, so I’m not going to put the cart before the horse. It sounds encouraging.”