Maxwell, 29, knows Seattle's defense well, having made 17 starts for the Seahawks from 2013 to 2014 before signing with the Philadelphia Eagles as a free agent. He was traded after one season to the Miami Dolphins, who released him in October.
He recently worked out for the Atlanta Falcons but was not signed, according to ESPN's Field Yates.
The Seattle Times first reported that Maxwell, along with former Seahawks cornerback Trovon Reed, will work out for the team. Reed has spent time on the team's practice squad and offseason roster.
Sherman was among several Seahawks injured in the team's victory over the Arizona Cardinals on Thursday night. His absence leaves the Seahawks with four cornerbacks on their roster: Jeremy Lane, rookie Shaquill Griffin, nickelback Justin Coleman and veteran Neiko Thorpe, who is primarily a special-teams player.
Another cornerback, DeShawn Shead, is on the physically unable to perform list while recovering from surgery to repair a torn ACL suffered in January. Shead, who had been a starter for a season and a half before his injury, has yet to begin practicing, so he is likely at least two weeks away from being able to play.
Maxwell was a sixth-round pick by the Seahawks in 2011 and appeared in 47 games during four seasons with the team before signing a six-year, $63 million contract with Philadelphia. The Dolphins are still on the hook for his $8.5 million salary this season, and he could be signed for a prorated share of the veteran minimum.
The Seahawks (6-3) host the Falcons on Monday Night Football in Week 11.