Kjell won his first game in charge this past weekend against ABC Motsepe League side EC Bees FC in the Ke Yona last-32 at Sisa Dukashe Stadium after drawing his first three games at the helm.
The Bucs have experienced a difficult season so far and Jonevret is trying to restore order, with this past weekend’s victory snapping a 12-game winless run, an unwanted record for a club that is regarded as one of the most successful teams in South African history.
The Buccaneers last won the trophy back in 2014, having lost in the final against Supersport United last year.
And Jonevret feels the 2017 Nedbank Cup may give the Sea Robbers the boost they have been looking for.
“I think everybody [hopes we can] do that but it's going to be difficult," said Jonevret, whose side will learn their last-16 opponents after Thursday’s draw in Randburg.
The Swedish coach also took heart from the fact the likes of Cape Town City and Ajax Cape Town have already been knocked out, increasing the possibility of earning a favourable draw.
He continued: ”If we can have a little bit of luck with the draw we could have many evenings [of football] if two, three or four first-teams are out. But there are still a lot of good teams [left in the tournament] so we have to be a little lucky also.
"But definitely it could be a chance [to revive hope] and that is the chance for Orlando Pirates to win something this season. Of course, we are going to go out one hundred percent for the cup, as long as possible.
"But as I said, as long as we are in the cup, you have a chance to win it, definitely. But this season, so far many teams in the PSL have been better than us.
"But since we started working [together] we are still undefeated in the league and the cup, but we are happy today. But of course, we have to be better if we want to play a cup final."
The upcoming FIFA-enforced break will see the former Djurgardens IF coach arrange a few friendly matches as their next competitive game will be on April 1, against Free State Stars at James Motlatsi Stadium in Orkney.
Since the 54-year-old took over he has had little time to look at the entire squad, and he admits he is glad to have the chance to get to know his team better.
"It's going to be one or two [clubs that Pirates face in friendlies] but I don't know [the identity of those clubs] right now. But we are going to have one or two," he added.