Varejao landed awkwardly in the third quarter of Tuesday's 125-104 win over the Minnesota Timberwolves and left the floor without being able to put weight on the leg. Initial tests couldn't determine the severity of the injury. League sources told ESPN.com that the Cavs fear one potential outcome is a torn Achilles.
Varejao left Quicken Loans Arena on crutches and with his leg immobilized in an air cast.
After the game, coach David Blatt provided little detail about Varejao's injury.
"He has an ankle injury of some sort," Blatt said. "I really don't know right now."
If Varejao is out for a significant period, it's believed the Cavs will intensify their monthslong efforts to trade for a big man. The team has been seeking additional help for its front line going back to the summer, having specifically targeted Timofey Mozgov of the Denver Nuggets and Kosta Koufos of the Memphis Grizzlies.
Sources say the Cavs, in recent days, have been in contact with the Boston Celtics about working as a facilitator in three-team trade scenarios. The Celtics, blessed with frontcourt depth in the wake of their recent acquisition of Brandan Wright in the Rajon Rondo deal, have been aggressive recently in their attempts to acquire future draft picks.
The Cavs cannot trade their own 2015 first-round pick because they already sent their 2016 pick to the Celtics in a previous deal. But they do own a protected Memphis first-rounder that they could trade.
The Cavs also possess a $5.2 million trade exception to use in a potential deal, which is one of the reasons they sought Mozgov and Koufos, as both of their contracts could fit into that exception.
The Cavs signed Varejao, who has missed 166 games with various injuries over the past four seasons, to a three-year, $30 million extension in October. He has been having a good offensive season as LeBron James' favorite pick-and-roll partner, shooting 55 percent from the field and averaging 10 points and 6.6 rebounds.
The Associated Press contributed to this report.