Britton will rejoin the Swansea squad for the first time since October for the visit of the Owls but it remains to be seen whether he will start on the bench or in the first team.
Andre Ayew and Andy King are both cup-tied as Swansea manager Carlos Carvalhal plans to rotate his squad. Wilfried Bony and Leroy Fer are out of for the season, while Angel Rangel and Renato Sanches remain on the sidelines.
Meanwhile, Carvalhal says the 4-1 defeat against Brighton in the Premier League at the weekend will not have an impact on his players, and also says they are not thinking about the forthcoming league clash against West Ham.
The Portuguese is full focused on the Wednesday game and is keen to book a place in the quarter-finals.
"The game against Brighton does not have any negative impact on the team - zero," the boss said.
"This game is completely different from Brighton. This is a cup game. We will try to win and then we will focus on West Ham."