Rice hasn't practiced all week after injuring his hip in the fourth quarter of the 14-6 win over the Cleveland Browns. But Harbaugh has previously said that the three-time Pro Bowl running back doesn't have to practice to play Sunday against the Houston Texans.
The Baltimore Sun, citing a source, reported Saturday that Rice has a left hip flexor strain that is regarded as a two-week injury.
On the official injury report released Friday Rice was listed as doubtful. Texans safety Ed Reed, who is working back from a hip injury, was listed as questionable. He hasn't played this season after coming over from the Ravens.
Rice has started 43 straight games, the longest current streak for NFL running backs.
"There's really nothing new to report," Harbaugh said. "We'll keep our fingers crossed, although we're prepared for it to go either way."
Backup running back Bernard Pierce wouldn't speculate whether he would start his first NFL game on Sunday.
"I try not to get involved with all the hype," Pierce said. "I just go out, stay focused and play my game."
Also Friday, the league said it would not discipline Rice after he was accused of spitting on Browns nose tackle Phil Taylor. Film of the play was inconclusive, according to the NFL.