Red Bull team boss Christian Horner told an FIA news conference at the Azerbaijan Grand Prix on Friday that he had proposed the idea at recent meetings of the Formula One Commission.
The last grand prix of the season is at Abu Dhabi's Yas Marina on December 8th.
Horner said it would be a fantastic opportunity to do something more meaningful than "just running around burning fuel and tyres and only the teams that are running those drivers knowing whether they're doing a good job or not."
The sprint format, with qualifying and a 100km race on the same day, would give potentially 10 drivers the chance to compete against each other in current cars without teams worrying about damage.
"I think it'll be a really popular event," said Horner.
Haas boss Ayao Komatsu, who has 19-year-old British rookie Oliver Bearman in his race line-up next year, was another in favour.
"I think it's great. You know, the post-season test, if we don't do things like that, you are just doing the tyre test. So I think it adds value to the day and makes it more exciting and another opportunity to put young drivers in the car," he said.
"These days, it's such a rare opportunity for young drivers to get in the current Formula One car. So I think it's really an interesting move."
Sauber representative Alessandro Alunni Bravi, whose team have the sole remaining vacancy for 2025, said it was important to provide more opportunities.
"Also for us, not having a TPC (Testing of Previous Cars) programme, it’s an additional opportunity to have more data and to assess not just the performance itself, also the mindset and the approach of the rookie driver."
Horner said there was a clear will to make the change this season, even if there were logistical challenges and other issues such as television coverage to be resolved.
"Obviously that puts pressure on the Sporting Working Groups and the various team managers to work with the FIA to come up with a set of regulations. But I think mainly adopting Sprint regs and so on, it's eminently doable," he added.
"It doesn't need to be over complicated. I think it's just going to be a single car from each team rather than two cars.
"And, effectively, you're just using the mileage in a different way... so I think the event will take place all in one day. So a qualifying and then the equivalent of a sprint race."