CSN Philadelphia also reported that while Asomugha's status for this weekend is up in the air, the injury does not appear to be season threatening.
The Eagles had no comment on the extent of the injury and a team spokesman said Asomugha's status would be updated on Friday.
Asomugha was participating in a non-contact drill on the grass fields adjacent to the team's NovaCare Complex when he was hurt.
"It's a short-lived career, and to see a guy go down, you just hope it's not as severe as what you saw initially," said cornerback Brandon Hughes, who would likely receive expanded playing time if Asomugha can't play Sunday. "That's what we're hoping."
Asomugha, who spent the 2003 through 2010 seasons with Oakland before signing a five-year, $60 million contract with the Eagles, has missed just six games in nine seasons.
Because Asomugha plays so many different roles -- outside corner, inside corner and safety -- it could be difficult for the Eagles to replace him with just one player. They have only one more practice before Sunday's game against the New England Patriots.
"We've got to stick to the game plan," strong safety Kurt Coleman said. "Nnamdi's definitely a big piece of what we do on defense, but we have guys we can rotate in, guys who can do similar things. Everybody has to step up their game if he can't go. Everybody has to pick up the slack."
Asante Samuel will start at one cornerback spot Sunday. The other healthy cornerbacks on the roster if Asomugha can't play are veteran Joselio Hanson, who has started 18 games for the 49ers and Eagles since 2003; Hughes, originally a fifth-round pick of the Chargers in 2009; and rookie third-round pick Curtis Marsh.
Hanson indicated Asomugha's injury might not be as severe as it originally appeared. "It looked bad but he'll be alright," Hanson said, via The Philadelphia Inquirer.
An injury to Asomugha would be a tremendous blow to a squad fighting to get back in the playoff hunt and already beset with injuries to cornerback Dominique Rodgers-Cromartie, quarterback Michael Vick and wideouts Jeremy Maclin and DeSean Jackson. Rodgers-Cromartie missed last week's win over the New York Giants with a high ankle sprain.
Vick (ribs) and Maclin (hamstring/shoulder) were held out of practice Thursday, while Jackson (foot) returned to practice on a limited basis. Maclin was limited in practice on Wednesday.
Rodgers-Cromartie and King Dunlap (concussion) also did not practice on Thursday.
The Associated Press contributed to this report.