Tuks are yet to record a win over United since gaining promotion last season, with SuperSport winning three of the four previous meetings.
Monyai, nevertheless, was upbeat about AmaTuks’ prospects in the knockout tournament.
“We prepare the same way for every league or cup game. We look to win every game that we play,” the 34-year-old veteran said in Johannesburg on Thursday.
“It will be good for the club to have a good run in the cup. We’ve got a young team and it will also give us a morale boost in the league. We haven’t beaten them yet.”
Tuks were knocked out at the first hurdle last season and will come up against the runners-up in SuperSport, who were edged after extra-time by Kaizer Chiefs in May last year.
With the tie taking place at the Tuks Stadium in Pretoria, Monyai admitted his relief at playing on home soil in the first round, which could be a catalyst for victory against their more fancied opponents.
“We’ve been doing well lately at home, we’ve struggled in our away games,” Monyai said.
“At home we’ve been like a bullet, we are a free-flowing team.”
Tuks have claimed six wins in the Premiership this season, all of which came at home and are yet to even score a goal on the road, let alone bag a win.
As a result, Monyai’s hopes of a positive result were boosted when the draw was announced last month, pitting the two Pretoria rivals together.
Monyai’s opposite number, Bevan Fransman, said it was up to SuperSport to bring an end to last season’s disappointment, where the team were beaten in two Cup finals, as they lost out on the MTN8, as well as the Nedbank Cup, under former coach Gavin Hunt.
“At SuperSport our ambitions are simple, to win trophies,” Fransman said.
“Last year we were twice losers in Cup finals, so this year we have to make up for games past and opportunities lost.
“We have to start with a win. We can’t really do much different. From my side, we need to keep a clean-sheet, number one.”