2:05pm: It doesn’t sound like the Rangers are getting any offers to their liking, as Heyman tweets that at this time, it appears that they may hold onto Gallardo.

10:17am: The Cubs and Blue Jays also remain in the mix for Gallardo, tweets Jon Heyman of CBS Sports. Those three teams are his main suitors, Heyman says, noting that the possibility of the Rangers retaining Gallardo still remains.

10:02am: The Dodgers and Rangers are having “ongoing discussions” regarding right-hander Yovani Gallardo this morning, reports Jon Paul Morosi of FOX Sports (Twitter link).

The 29-year-old Gallardo was an offseason acquisition by the Rangers, who acquired him from the Brewers in exchange for Luis Sardinas and Corey Knebel. He’s had a nice season overall with Texas, notching a 3.39 ERA 6.0 K/9, 3.4 BB/9 and a 49.5 percent ground-ball rate. However, Gallardo’s recent performance hasn’t done the Rangers any favors in terms of trading him; he’s allowed five runs in three consecutive starts.

Gallardo’s strikeout numbers are way down from his 2009-11 peak, but his ground-ball rate is up, and his control numbers have sharpened as well. He’s earning $14MM this season in his final year of control before hitting the open market. Clearly, a trade would benefit his free agent stock, as he’d be ineligible for a qualifying offer.

The Dodgers have already added Mat Latos and Alex Wood to their rotation, though there have been indications that they’re still in the market for even more rotation help despite those trades.