Berkman took batting practice Tuesday and the soreness in his surgically repaired knee has improved after sitting out a weekend series against the Cincinnati Reds.
Berkman wasn't ready to push it in time for Tuesday's series opener against Seattle.
"We'll give it another day," Berkman said.
The Rangers are happy enough with Berkman's improvement that they don't expect him to need a stint on the 15-day disabled list.
"We're content he's making progress," Rangers manager Ron Washington said.
What's the confidence level on Berkman being able to play Wednesday?
"Confident?" Washington asked. "I can't say that. But I hope so."
Berkman hasn't played since Wednesday at New York when he had two singles in his final two at-bats against the Yankees. He had been in a 2-for-22 slump before that as his season batting average has dipped to .263.
Berkman had a scheduled day off Thursday against the Yankees. The Rangers had a three-hour delay before they flew back to Texas on Thursday night and arrived just after midnight Friday morning. Berkman slipped down a flight of stairs upon their arrival.
He's had four surgeries on his right knee and has been dealing with soreness at various points all season.