The pair, who have won nine of the last 10 Grand Slam titles between them, will meet in the Hyundai Card Super Match at the Inspire Arena on Saturday, eight days before the Australian Open begins at Melbourne Park.
"It was once or twice we thought about it," world number one Alcaraz told a press conference on Friday, which was followed by a playful table tennis session in front of hundreds of fans.
"But being singles players and playing so many matches, tournament after tournament in a row, it's really difficult to play doubles sometimes.
"At least once would be fine. But I think I play forehand and he (Sinner) plays backhand."
Sinner also embraced the idea.
"I think it would be fun at least one time to share the court in different ways, on the same side," he said.
"We are going to talk about it maybe this year. Or next year. Why not? It's going to be a surprise!"
'Our own story'
The duo, dubbed "Sincaraz", have helped usher men's tennis into a new era beyond the Big Three of Roger Federer, Rafa Nadal and Novak Djokovic.
"We have a great rivalry. We also need to see how long we can keep up this level. What the Big Three has done, we cannot compare ourselves with them. We also don't want to. We are just ourselves," world number two Sinner said.
"We want to make our own story. It's how everything should be. In sport, we should not compare so much because everyone is different. I'm happy to be part of this two at the moment.
"There are many great other players and if we drop just a little bit, they're going to take our place. It's great to have him to push me to the limit."
Sinner stressed that their performances in the Seoul clash would not be a true indicator of how they will fare at the Australian Open.
"We're happy to be here, we're happy to provide hopefully good tennis tomorrow," the Italian added.
"But it's not going to reflect on any of us how we're going to start the tournament in Australia. We are here to make hopefully a good match, but also to put a smile on as many people as possible."