Baker is also dealing with a strained groin muscle/sports hernia that limits him to designated-hitter duty.
"It's good enough to swing, and the running part is getting better," Baker said.
Baker said he is hoping to be ready to play the field in the postseason if needed and is expecting to be available all through October, if necessary.
"Yes, 100 percent," Baker said. "I will be able to play. I feel like it is getting better. I have had a lot of medicine and a lot of shots down there. I think it's all helping a little bit."
The Rangers could get Nelson Cruz back for the playoffs, but right now they don't have a lot of right-handed options to use against left-handers. The Rangers have given up on the idea of using either Jurickson Profar or Lance Berkman as switch-hitters from the right side. With Baker limited to designated-hitter duty, left-handed-hitting Mitch Moreland continues to start at first base.
Moreland went into Wednesday hitting .240 with a .419 slugging percentage against left-handers. But he also had four hits in his last 11 at-bats against them including a big home run off the Rays' Matt Moore last Thursday in St. Petersburg.
"My options are limited, so I put him in there," Washington said. "He may catch one. He is my best first baseman, so I'm going to take my chances and see what happens."
T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, and follow him on Twitter @Sullivan_Ranger. Master Tesfatsion is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.