The Rangers pursued Lee vigorously last year at the Trade Deadline before the Indians dealt him to the Phillies.
Assistant general manager Thad Levine, who is with the team in Florida, declined to discuss specific names but did acknowledge the Rangers' pursuit of pitching.
"We've had some preliminary discussions with clubs," Levine said. "But to compel teams to move this far ahead of the [July 31st] Trade Deadline, it would take a very attractive package," Levine said. 'We're still in the inventory stage and the information-gathering stage rather than the execution phase."
The Rangers cannot take on significant payroll in any trade. But they can get other teams to pick up a high-priced player's salary if they add extra prospects to the package. The question is if the ownership situation will be resolved by the Trade Deadline. If the Ryan-Greenberg group takes over before then, the Rangers will have financial flexibility to add payroll in any trade without giving up additional prospects.
The Rangers are trying to keep their rotation together, but it has been difficult. Derek Holland (rotator cuff inflammation) and Rich Harden (strained gluteus muscle) are on the disabled list, and Tommy Hunter had to come out of Wednesday's start after 2 1/3 innings because of a strained right hip flexor muscle.
Hunter said the muscle was better on Thursday and will test it off the mound in a bullpen session on Friday in Houston. The Rangers will know after that session if he can start Tuesday against the Pirates.
The Rangers did not make a move on Thursday, but Guillermo Moscoso was pulled from his start at Triple-A Oklahoma City. He could be called up on Friday if the Rangers need pitching reinforcements.
The club's concern about starting pitching is altering its plans with Brandon McCarthy, who has been sidelined with a stress fracture in his right shoulder blade. He is close to coming off the disabled list at Oklahoma City.
The Rangers had plans to moving him to the bullpen. Now, they are going to get him back in the rotation to increase their starting rotation depth.
"At the outset of the season, we felt one of our strengths was the depth of our starting rotation," Levine said. "Unfortunately, over the last few weeks we've seen a significant erosion of that depth."
Holland could be back soon. He is scheduled to throw in the bullpen on Saturday in Arizona. If that goes well, the next step could be a medical rehabilitation assignment in Oklahoma City next week.
"His return isn't imminent, but the good news is Holland should be back in the near-term." Levine said.