10:19am: Sullivan now says that nothing has come of recent chatter (on Twitter). Gallardo is more of a “fallback” for the Jays, tweets Evan Grant of the Dallas Morning News.

10:18am: The Blue Jays are interested in Rangers starter Yovani Gallardo, MLB.com’s T.R. Sullivan tweets. He notes that there is a real possibility of a deal coming together.

As it shops the veteran righty, Texas is hopeful of finding a right-handed bat, Jeff Wilson of the Fort Worth Star-Telegram adds (Twitter links). Notably, per Wilson, Gallardo would be willing to waive his no-trade protection to facilitate a deal to Toronto.

Gallardo is set to start tonight for the Rangers, so there could be some impetus towards getting something done in the near term. After adding Cole Hamels yesterday, Texas may be looking to recoup some value. But Wilson does note that the Rangers could hold on to the right-hander, with the idea of possibly making a late-season playoff run and getting value back from him through the qualifying offer system.