The Italian team want the 39-year-old Briton to partner current driver Charles Leclerc, according to the BBC, Sky, Autosport, Italian newspaper Gazzetta dello Sport and other media.
It would be a surprise move given that Hamilton has signed a two-year contract with his current team Mercedes for the 2024 and 2025 seasons, but the deal reportedly contains a clause allowing him to leave after one season.
Hamilton won the last of his world titles in 2020 but lost the 2021 championship in controversial fashion to Max Verstappen when the race director ignored the safety car rules, effectively blocking the Briton's route to victory in both that grand prix and the championship.
The Dutch Red Bull driver, who is 13 years younger than Hamilton, has dominated ever since.
Hamilton finished sixth in the drivers' standings in 2022 and third in 2023.
Ferrari, who have admitted they held discussions with Hamilton in 2019 about joining them in the future, declined to comment on the reports they were negotiating a switch for the 2025 season.
A Ferrari spokesman said: "We do not comment on rumours.”
Mercedes did not reply when contacted by AFP.
Hamilton has never hidden his anger at the 2021 incident, believing he was robbed of an eighth title that would have put him on one more than Ferrari legend Michael Schumacher.
He has made clear his frustration with the performance of his Mercedes car in the last two years and might believe a move to Ferrari would enable him to reignite his challenge for that elusive title.
However Ferrari have also suffered patchy form in the last few seasons although they seemed to find momentum towards the end of the 2023 season.
That improvement was not enough to prevent Mercedes beating them to second place behind Red Bull in the constructors' championship.