This comes after the news that starting right tackle Phil Loadholt is out for the season due to a torn pectoral muscle.
Winston, 31, signed on with the Seahawks back in late July after finding very little interest as a free agent. However, he was unable to make the final 53-man roster coming out of the preseason.
The Eagles later brought him in for a workout, but wound up going in a different direction.
Last year, Winston appeared in all 16 games for Arizona, but graded out as the No. 69 tackle in the league, according to Pro Football Focus.
Webb, 26, is a former seventh-round pick of the Chicago Bears back in 2010. He spent three years in Chicago before he was waived and later claimed by the Vikings.
As an unrestricted free agent this past offseason, Webb signed a one-year contract with the Chiefs, but he was unable to make their final roster at the start of the regular season and was subsequently released.