Pirates, who are 11th on the Absa Premiership table with 10 matches left, were last night pitted against Wome's ex-club Free State Stars in the last-16 of the cup.
The tie will be played between April 5-9, with the exact dates, times and venues to be announced by the PSL in due course.
The teams will first meet in a league fixture on April 1 at James Motlatsi Stadium.
“We will be playing both games away from home which will not be easy so we need to be prepared,” Wome is quoted as saying on Bucs' website.
“Free State Stars are a very good side especially when it comes to cup matches as they have shown recently when they knocked out Kaizer Chiefs in the Telkom Knockout. Playing them back-to-back offers a different challenge…it’s easy for a team to fall into the trap by focusing on one competition over the other but not us. We will take it one game at a time and hopefully we can be successful in both.
“This is our last chance to win silverware for our supporters so we will be taking it very seriously. We want to get back to playing continental football and this is one competition which gives us an opportunity to do so,” added the Togo international.
The Nedbank Cup champions automatically qualify for next season's CAF Confederation Cup.