"We definitely want to make sure we are prudent and these guys have ample time to be ready," Banister said. "It's about 162 (games) and not one."
Fujikawa reported the tightness in his groin muscle after pitching against the Cubs on Tuesday. Fujikawa allowed five runs in just one-third of an inning. It was his seventh outing of the spring.
Scheppers has a sprained right ankle. An MRI showed no structural damage and Scheppers will be re-evaluated this weekend but he has only pitched 32/3 innings this spring so there is concern that he has not built up enough arm strength to be ready for Opening Day.
Tolleson has been dealing with tightness in his right forearm but has pitched two scoreless innings in B games on Sunday and Tuesday. He might be closer than Scheppers and Fujikawa to being ready for Opening Day but the Rangers haven't decided if he'll pitch either Friday or Saturday against the Mets.
"We'll let that play out," Banister said. "We still have time. That's in our best interests. We need to give those three the opportunity to see how they show up this weekend."
Right now the only pitcher assured of being in the bullpen on Opening Day is closer Neftali Feliz although the Rangers expected recently-acquired left-hander Sam Freeman to be there as well. The Rangers do have five healthy relievers still in camp with right-handers Jon Edwards, Roman Mendez, Phil Klein and Keone Kela and left-hander Alex Claudio. Starters Lisalverto Bonilla and Anthony Bass are still in camp as well.
T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, and follow him on Twitter @Sullivan_Ranger. This story was not subject to the approval of Major League Baseball or its clubs.