Giambi, 42, was in the Indians' starting lineup Saturday for the first time this spring, serving as the designated hitter and batting cleanup against the Reds. Cleveland is giving the aging slugger a chance to win a spot on the Opening Day roster as a part-time DH, first baseman and pinch-hitter.
All the Indians have asked of Giambi -- a non-roster invitee -- is to be honest about how he feels.
"We're trying to monitor his at-bats, because I don't want to run him into the ground," Indians manager Terry Francona said. "But that's like everybody. But again, with guys that have some age on them, you use some common sense. He's smart enough. I told him, 'Tell me when you're good.'"
Francona said he believes Giambi still has good bat speed.
"I don't think that's a concern," Francona said. "We just want to make sure it's a fit on the ballclub. His bat speed is fine."
With the Rockies, Giambi collected 26 at-bats last spring and 31 at-bats in Spring Training two years ago. Over the past three seasons as a role player off Colorado's bench, Giambi hit .245 with a .370 on-base percentage, 20 home runs, 72 walks and 75 RBIs in 211 games.
If Giambi makes the Tribe's roster, it will mark his 19th season in the big leagues.
"He's been doing this for a long time," Francona said. "When you watch him hit, he's got it down to such a simple swing. He's got a little movement forward. He's got a pretty good idea of what he's doing."
Jordan Bastian is a reporter for MLB.com. Read his blog, Major League Bastian, and follow him on Twitter @MLBastian. This story was not subject to the approval of Major League Baseball or its clubs.