Odrick was on the verge of returning from a broken right leg when he hurt his left foot at the end of practice Wednesday.
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The Miami Herald reported Thursday that Odrick suffered a fractured leg, but the newspaper didn't specify which side.
The Dolphins haven't decided whether or not to put the rookie on injured reserve, which would end his season.
"We'll see," Sparano said. "Right now, we're going to sit tight for a little while."
Odrick worked with the first team from the start of training camp, but he has been sidelined since he sustained a slight leg fracture in the season opener. He also broke his right leg in 2007 and missed the rest of that season with Penn State.
Sparano declined to reveal details about the nature of Odrick's latest injury. The lineman, taken with the 28th overall pick in the April draft, has one tackle this season.
"He's a heck of a player," Sparano said. "He's a guy we certainly could have used. That being said, there are guys who have stepped up and done a nice job."
The Associated Press contributed to this report.