"I'm moving in the right direction, but there's still some maintenance stuff to do," Cannizaro said.
The infielder test-ran his back on Friday, taking batting practice and ground balls with the team.
Manager Joe Maddon said if all went well during pregame warmups, Cannizaro would start in Saturday's game vs. the Pirates.
In addition to Cannizaro, the Rays are hoping to pencil infielder Willy Aybar and backup catcher Shawn Riggans back into the lineup.
Aybar was sidelined for several days due to tightness in his left hamstring, but he reported to be feeling better on Friday. Riggans, who suffered a bruised left hand after being hit by a pitch on March 15, took some swings in Friday's Minor League game.
Maddon said Riggans reported that everything "felt right," and he will likely start Saturday's game.
Center fielder B.J. Upton also made his case to play on Saturday.
Upton, who suffered a left tricep contusion in the first inning on Thursday after being hit by Indians pitcher Paul Byrd, told the media on Friday that the initial sting is gone, and he felt fine when he woke up.
"I don't know if they're going to let me, but I'm looking to [play] tomorrow," Upton said.
Although Maddon had initially wanted to give the center fielder another day of rest, the Rays manager changed his tune when he heard Upton's remarks.
"He could talk himself into it," Maddon said. "It's [just] a bruise and if he wants to ... if he makes a compelling argument."
Akinori Iwamura, who also had an early exit in Thursday's game, will take the extra day of rest.
Iwamura was removed in the third inning after citing back soreness, and Maddon said that the Rays will exert caution and hold Iwamura out until Sunday.
Iwamura said he would be ready to go by then, and he noted that the tightness was minor.
"If it were the regular season, I would play. No problem," Iwamura said.
However, Rays No. 1 starter Scott Kazmir is still unsure about when he will return.
Kazmir played catch with athletic trainer Ron Porterfield on Friday and said there is no specific timetable on when he will throw off a mound.
Kazmir, who suffered a left elbow strain on Feb. 25, has not thrown off a mound since March 13, and the Rays continue to remain vague about his status.
Maddon did say that Kazmir was feeling better after Friday's catch session, and the Rays will continue to evaluate his progress on a daily basis.