Grabow had a side session Monday in Mesa, Ariz., and all reports were good.
"He had a smile on his face, and a smile from all who watched it and were around it," Cubs manager Mike Quade said.
If Grabow passes all the tests Tuesday, he was expected to pitch one inning when the Cubs travel to Phoenix to face the Athletics on Thursday.
Quade said there is plenty of time for Grabow to get prepared for the regular season. Depending on whether James Russell is in the rotation or not, the Cubs will likely have at least three, and possibly four, lefties in the bullpen with Grabow, Sean Marshall and Scott Maine in the mix.