DETROIT -- The Tigers' patience could yet pay off with a closer at the end of their offseason dealings. But it appears it could be a wait.

While the Tigers have shown interest in free-agent closer Jose Valverde, so have other teams, to the point where Yahoo Sports reported that four offers are in for the two-time former National League saves leader.

It wasn't clear whether one of those offers came from the Tigers, or how recently those offers came in, but it's becoming clear nobody has met Valverde's reported asking price. The former Astros closer stands as the most prominent of the few closers left on the market, but he could remain there for a while in a waiting game until either a team or the pitcher budge.

ESPN.com's Buster Olney suggested Friday morning that Valverde was looking for $8 million per year, following other reports in the same financial range. His desire for a multiyear deal was strong enough that he declined Houston's offer of arbitration last month.

Neither the Tigers, nor the D-backs -- who are believed to be at their budget -- nor any other clubs in the market for a closer appear to be in that kind of financial range. In the Tigers' case, their abundance of young relief talent -- including closing prospect Daniel Schlereth from last month's trade of Edwin Jackson -- has given them another reason not to pursue a longer-term deal for any closer. There were indications the Tigers might've been a little more willing to consider a second year when they were talking about their own free-agent relievers, including Brandon Lyon, but both Lyon and Fernando Rodney signed elsewhere.

Tigers president/general manager Dave Dombrowski said earlier this week that he's "content" with his club's bullpen options if they don't sign anybody else, leaving Ryan Perry and Joel Zumaya as the likely competitors for the closing job. However, Dombrowski also said he's "open-minded" about finding ways to improve if any moves make sense.

From an experience standpoint, at least, adding Valverde has logic for a team where Zumaya's four career saves make him the most accomplished closer on the roster. Valverde's 116 saves over the past three years tie him for fourth in the Majors in that span with Jonathan Papelbon, trailing just Francisco Rodriguez, Joe Nathan and Francisco Cordero.

Valverde had just 25 saves and 45 games finished last year, but his supporting numbers were basically as strong as usual. He scattered 40 hits over 54 innings, struck out 56 and allowed just five home runs to go with his 2.33 ERA. He turned 30 years old last July.

Valverde has never pitched in the American League. He spent his first five years with the D-backs before he was traded to Houston after the 2007 season. However, Lyon didn't have much AL experience, either, until his '09 season in Detroit.

One complication would be the cost of a draft pick. Signing Valverde, a Type A free agent, would cost the Tigers' their first-round selection in this June's First-Year Player Draft. Though Detroit has two compensation picks coming from the loss of Lyon and Rodney, those picks won't be until the end of the first round. Even for a team that has found talent out of its secondary picks, that's a heavy price to pay.

Though Tampa Bay managed to add a similar Type A free agent reliever, Rafael Soriano, without giving up a draft pick in a sign-and-trade deal with Atlanta, such a move isn't likely to be repeated in this case. The Astros are expected to value the picks over any talent an interested club might offer.

The Tigers have a policy of not commenting on specific free agents.

On another front, Dombrowski said the Tigers were not in heavy pursuit of outfielder Scott Podsednik before he signed a one-year deal with the Royals on Friday. Though Podsednik spent time in center field last year with the White Sox, the Tigers did not consider him an option in center.

"We did not really pursue that," Dombrowski said.

Despite other rumors percolating, Dombrowski said the Tigers aren't looking to add a hitter unless that player has a defensive skill set. A rumored sighting of Jim Thome in Detroit last week fueled speculation of potential interest, but that won't be happening.

"We're not looking to add a DH," Dombrowski said. "We've said that all along."

Dombrowski reiterated the Tigers' plan to have Carlos Guillen and Magglio Ordonez rotate in the designated hitter spot on days when they aren't in the outfield, allowing Ryan Raburn and Clete Thomas to potentially have some sort of semi-regular role. Miguel Cabrera also could see some limited time there, too, though he remains the everyday first baseman.

That said, Dombrowski isn't ruling out adding a hitter. After all, he admitted, "It's not like we led the league in runs."

The Tigers could add a hitter, Dombrowski said, "if it's the right situation. But it would have to be the right guy."