Sundowns beat Ghanaian side Medeama SC 3-1 in their first leg CAF Confederation Cup play-off tie at the Lucas Moripe Stadium last weekend.
According to the Cape Town-born Arendse, the team is brimming with confidence after wirapping up the Absa Premiership title with two games to spare.
"The hard work starts now for us," Arendse tells snl24.com/kickoff.
"It's high time that teams from South Africa start staking their claim on the African continent. We have acquired success and this makes us hungry for more.
"We have to dream bigger now and set higher goals. We definitely have the squad to give it a good run."
The former Santos defender has done well to fill the vacancy of former captain and Dutch defender Alje Schut, and has paid tribute to coach Pitso Mosimane for instilling the belief in him.
"Pitso is a top class coach and he just proven that yet again [by winning the league title]. The coach deserve a lot of praise for the way he has managed the players this season," he adds.
"I think we can achieve more – like winning the Confederation Cup perhaps – who knows? But it's imperative that we dream big and go out to make things happen."
The Chloorkop-based outfit face a lengthy trip for their return leg against Medeama on Wednesday evening, with the team set to depart on Sunday evening.