"We had a good visit," head coach Joe Gibbs said on Thursday. "We think he would fit in at a number of places. He's very versatile. He's played corner and safety.
"I think he's going to consider his options. We're trying to give him a feel for what the Redskins are about, but we'll see what happens down the road."
Along with the Redskins, McQuarters is expected to visit several other teams before making a decision.
McQuarters was released by the Chicago Bears on May 23.
McQuarters, 5-10 and 195 pounds, is a seven-year veteran who was a first-round draft choice (28th overall) of the San Francisco 49ers in the 1998 NFL Draft. He was traded to the Bears prior to the 2000 season and played under current Redskins coaches Greg Blache and Dale Lindsey in Chicago.
"Our coaching staff knows a lot about him," Gibbs said. "So we think we have a good feel for him."
During his career, McQuarters has appeared in 99 games with 58 starts and recorded 386 tackles (288 solo), 10 interceptions and two sacks. Last season, he started 14 of 16 games and amassed 80 tackles, two interceptions and eight pass deflections.
McQuarters also excelled as the Bears' primary punt return specialist last season, running back 44 punts for 435 yards and one touchdown.