Coach Doug Pederson would not confirm the report during his news conference on Monday, saying he is still gathering information.
A team source confirmed that Darby received the best possible diagnosis, and doctors believe he is in a 4-6 week timeframe to rehab and return. The team has encouraged Darby to get a second opinion, and Darby is expected to see Dr. Robert Anderson, a foot and ankle orthopedic specialist in Charlotte, North Carolina, the source added.
Kicker Caleb Sturgis, meanwhile, injured his hip early in the season opener against Washington on Sunday and is expected to miss time. A source told ESPN's Adam Schefter that Sturgis is expected to miss four weeks. Pederson said the Eagles will work out kickers this week.
Darby was carted off the field with an air cast on his lower leg in the second quarter of the Eagles' 30-17 victory over Washington. His ankle bent awkwardly as he planted while in coverage, and he immediately went down in pain.
Surgery would have meant that Darby would miss the rest of the season.
A 2015 second-round pick out of Florida State, Darby finished second in voting for defensive rookie of the year in 2015 before taking a bit of a step back last season. Asked what he liked about Darby, Eagles executive Howie Roseman pointed to "rare speed" -- Darby ran a 4.38-second 40-yard dash at the scouting combine -- as well as his production on the ball. He has only two career interceptions but has 33 pass breakups in 29 games.
ESPN's Tim McManus contributed to this report.