Tolleson hasn't kept up with them because of some early tightness in his lower back. He has pitched in three Cactus League games and allowed one run in 2 2/3 innings on three hits and three walks.
"I think he's really close," Banister said. "He's still got a minor rhythm kink that I know [Tolleson] will work out. The stuff is there. We've still got some time for him to log innings and pitches to get ready. I feel confident Tolleson will find his rhythm."
Tolleson led the Rangers with 35 saves last year and goes into the season as Texas' closer, although there may be certain times where Banister may alter the plan depending on circumstances.
"Shawn Tolleson will close for us…yes," Banister said. "He was pretty good, more than pretty good. I'll give him the opportunity to continue that."
Ryan Rua: Everybody seemed to forget about Rua during the mad rush to find alternatives in left field and first base. Justin Ruggiano was signed this offseason to be the right-handed platoon partner with Josh Hamilton in left, and then Drew Stubbs and Ike Davis were signed at the beginning of camp for more first base/outfield depth.
Finally, when it was obvious that Hamilton would not be ready for Opening Day, the Rangers signed Ian Desmond to play left.
All those moves seemed to push Rua deeper down the chain, but that hasn't kept him from having an outstanding spring. He entered Thursday hitting .450 (18-for-40) with six doubles, a triple and a home run.
Rua could still win a spot on the bench as a fourth outfielder if Desmond proves he can play center field if needed.
Sam Freeman: This is going to be a tough call for the Rangers. Freeman was an integral part of the Rangers bullpen last year as a versatile left-hander who could be used in specific situations or for multiple innings.
He averages 93.8 mph and held right-handed hitters to a .167 batting average last season. He is also out of options, meaning he would have to clear waivers before being sent to the Minors. Clubs covet hard-throwing left-handed relievers.
Freeman's spot is in jeopardy because Andrew Faulkner has had a great camp. The Rangers could still keep Freeman as the eighth reliever or send Faulkner down because he has options.
Chris Gimenez: He was magical in 2015 as the catcher who rescued the Rangers in the final two months of the season. But now, Gimenez is in a fight for the No. 2 catching spot with Michael McKenry and Bobby Wilson. All have Major League experience and come with strengths and weaknesses.
McKenry and Wilson have outs in their Minor League contracts, meaning they can take their free agency if they are not on the Opening Day roster. Gimenez is out of options, and could also take his free agency if he clears outright waivers.
The Rangers' primary objective is to identify the catcher who can handle the defensive responsibilities and work with the pitching staff.
Jeremy Guthrie: He has far and away the most experience of the Rangers' fifth-starter candidates. But the competition is still fierce and time is running out. So are innings.
"It's time for everybody to start executing pitches," Banister said. "That's what we are looking for."
Guthrie also has an out in his contract at the end of Spring Training if not added to the roster.