Ferrari needs "two experienced drivers" for 2021, according to team boss Mattia Binotto.
Just before Christmas, the Maranello team announced that Charles Leclerc's current contract has been extended for two more years, taking the new deal to the end of 2024.
La Gazzetta dello Sport claims the deal involves a tripled salary for the 22-year-old.
But it also leaves Sebastian Vettel exposed, as the German's deal runs out this year.
"It is rarely a good move to leave a winning team," he said. "And Lewis would not have enough time to build a new team alongside Leclerc."
Ferrari CEO Louis Camilleri says the Hamilton rumour has been "overblown", even though he admits the British driver met with chairman John Elkann.
"The two met at an event as they have mutual friends, but it's far too early to talk about drivers for 2021," he said.
"Our situation is well known. We have a driver with a long-term contract and a second driver whose contract expires at the end of 2020."
Camilleri says Ferrari will "review" the situation later this year, but what is certain is that Mick Schumacher or the other Ferrari juniors will not get a call-up for 2021.
"That would be too early for them," said Binotto. "For an important year like 2021, we need two experienced drivers."