UPDATE: Gallardo might not be going anywhere...

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Yovani Gallardo will be a free agent after the season and it's not entirely clear whether or not the Texas Rangers are going to trade him. There's certainly a market for the right-hander, who is garnering interest from multiple MLB teams.

The latest rumors find the Chicago Cubs, Los Angeles Dodgers, Toronto Blue Jays, New York Yankees and San Francisco Giants are in pursuit of Gallardo, according to Jon Heyman of CBS Sports. The right-hander, who was acquired from the Milwaukee Brewers in the offseason, is 7-9 with a 3.39 ERA, 1.34 WHIP and 84 strikeouts in 22 starts (127 1/3 innings) this season.

The Rangers, according to ESPN's Jerry Crasnick, are telling teams they are willing to keep Gallardo for the remainder of the season and receive draft pick compensation when he likely signs with another club after rejecting the Rangers' qualifying offer. However, there is heavy interest in him right now and they might get some good offers, so let's take a look at each club eyeing Gallardo.

Los Angeles Dodgers

The Dodgers made an enormous 13-player trade in a three-team deal yesterday with the Miami Marlins and Atlanta Braves. Los Angeles received starters Mat Latos and Alex Wood in that transaction, which is likely all they need considering now that their rotation is full with those two, Clayton Kershaw, Zack Greinke and Mike Bolsinger. Unless they make another move to clear space for Gallardo, the Dodgers don't seem to be a top destination for the right-hander.

But hey, you never know...

Chicago Cubs

The Cubs are in serious talks with the San Diego Padres regarding starters Tyson Ross and Andrew Cashner. It's been said they aren't in the market for rental players because they don't want surrender prospects for someone who isn't guaranteed to remain with the team after the season, which is why Ross (signed through 2017) and Cashner (signed through 2016) are on their radar. It's more likely they make a trade for a starter they can control beyond 2015 and then work to sign a high-price free-agent starter in the offseason.

"The Cubs have looked at Yovani Gallardo but have generally been linked to pitchers who are under control into 2016, so they may not be a favorite," Heyman added.

Toronto Blue Jays

We can't rule them out of anything. After acquiring Troy Tulowitzki from the Rockies and David Price from the Tigers, FOX Sports' Jon Morosi says the club is still looking for a starter. Toronto is interested in Tyson Ross and Carlos Carrasco of the Indians as well. They were in the market for Cincinnati Reds' starter Mike Leake, but he was traded to the Giants last night, so it's very possible Gallardo lands with the Blue Jays before 4 p.m. today. General manager Alex Anthopoulos still has resources left in the farm system to make a deal, and at this point he's not going to hesitate as it appears the club is in it to win it in 2015.

New York Yankees

At this point, New York seems like the top destination for Gallardo. The Yankees have been dealing with issues in their starting rotation (4.36 ERA) and the team placed Michael Pineda on the disabled list yesterday with a mild forearm strain. That same injury kept closer Andrew Miller out for a month. And now with the Blue Jays making astute additions to their roster as they sit six games behind New York in the AL East, the Yankees need to ensure they are prepared for down the stretch because their rotation is inconsistent and injuries can affect just about any starter on their staff.

Here's an indication Gallardo could be in their crosshairs:

San Francisco Giants

The report of the Giants' interest in Gallardo came before they landed Mike Leake in a trade last night. They paid a fairly steep price for Leake by giving up prospects Keury Mella and Adam Duvall, so it's likely they are done making deals, at least for starters. Leake will join Madison Bumgarner, Chris Heston, Jake Peavy and Matt Cain in the Giants' rotation, which leaves no room for Gallardo unless the team trades one of their other starters (something that hasn't been speculated and is probably not happening).

Gallardo might stay with the Rangers when the clock strikes 4 p.m. today, but keep an eye for the Yankees or Blue Jays to make a move for the right-hander before then.