The Raiders have discussed placing Lynch on injured reserve but no decision has been reached, the source said.
The news was first reported by NFL Network, which said Lynch would be sidelined for at least a month.
Lynch has rushed for a team-high 376 yards on 90 carries (4.2 yards per carry) and three touchdowns this season. He also has 15 receptions for 84 yards.
ESPN's Dan Graziano contributed to this report.