Sweat went on injured reserve Nov. 13 after a non-displaced fracture of his jaw in a Week 8 game against the Broncos.
He was expected to return last week against Dallas but tested positive for COVID-19. Sweat, who is unvaccinated, spent 10 days on the list before being activated from it Saturday.
So he now is preparing to return Tuesday night.
Sweat has totaled four sacks, 12 quarterback hits and three tackles for loss this season.
Cosmi has started six games for Washington this season but missed time early in the season with an ankle injury.