Williams suffered a sprained left ankle on Seattle's first offensive possession and did not return in Sunday's 31-14 win over the Carolina Panthers.
Williams's health situation "is not good," according to the source. The Seahawks do not see placing Williams on injured reserve at this time, but there is speculation that he would be held out past the team's Week 14 game against the San Francisco 49ers.
Already nursing a left foot strain that kept him out of Week 12's loss to the Kansas City Chiefs, Williams was rolled up on while blocking on a run play against Carolina. Williams' was engaged with a Panthers defensive back when Seahawks running back Justin Forsett fell into his legs.
Williams, with his fourth team in five seasons, has thrived in Pete Carroll's system, catching 52 passes for 654 yards and a touchdown, his best numbers to date. Williams has 96 receptions for 1,193 yards and three touchdowns in his career with the Detroit Lions, Oakland Raiders, Tennessee Titans and Seahawks.
The Associated Press contributed to this report.