Already a member of the Ferrari driver academy, the rumour mill is hinting strongly that the impressive 20-year-old rookie is being lined up to replace Kimi Raikkonen.
"It's nice to see such a talented young driver developing so well," Liberty Media F1 chief Ross Brawn said.
Raikkonen is not even denying that he could in turn move to McLaren.
"I have zero interest to get involved in all the nonsense," he told reporters in Austria when asked about the speculation.
For his part, Monaco-born Leclerc said he has heard the rumours but is preferring simply to focus on his work at Sauber.
"I don't think about it too much, although that is difficult.
"I see the rumours and it makes me happy because it has always been my dream to drive for Ferrari. If one day it happens, it would be just amazing."
Leclerc has earned 11 of Sauber's 13 points in 2018.