Stoinis was sore after Australia's first match of their 2-1 series defeat by India last month and skipped two warm-up games and the loss to the hosts in the World Cup, but Cummins said he will be looked at closely for Thursday's clash.
Stoinis plays for the Lucknow-based Super Giants in the Indian Premier League (IPL) and knows the conditions well.
"He's fit so yeah, we'll announce a team tomorrow but it's a ground he knows pretty well," Cummins told reporters.
"I think chatting to him and a couple of other guys, it's probably in a bit of a different condition to what it is for the IPL. The wicket looks really good so yeah, he's someone we'll look at pretty closely."
Australia were dismissed for a below-par 199 in their first match, before suffering a six-wicket defeat by India in Chennai, but Cummins said he expects a high-scoring game in Lucknow.
"When it's a good wicket - which that looks like - most of the games have been 300 plus," Cummins said.
"I haven't had a look at it today, but last night it looked really good, really even. Maybe a bit of pace and bounce. We'll see how it is tomorrow."
Australia's specialist spinner Adam Zampa went wicketless in the last game and gave away 53 runs from eight overs but Cummins said critics should not look too deeply into his form.
"I thought he bowled okay but it's pretty hard defending 200 and trying to create something out of nothing. I'm sure he would be great out there," Cummins said.
"Again, if you have a bit more of a total to bowl to, he's one of our key guys."
Five-times champions Australia will be wary of South Africa, who made 428-5 in their opening win over Sri Lanka with three of their batsmen - Quinton de Kock, Rassie van der Dussen and Aiden Markram - smashing centuries.
The Proteas boast an enviable top-order but De Kock called for more consistency in World Cup matches.
"We're doing really well as a batting unit; we've worked really hard on our game the last couple of years. It's only one game into the World Cup, so it's hard to say how we're really going," De Kock said.
"Even though we've had it really well our last couple of games, it hasn't been over the course of years. It's only been a course over a month or a couple of months.
"So in order for us to be one of the best we need to be, we still need to be a bit more consistent especially in tight games like World Cups. That will determine actually how good we are."
