MGM is one of Hollywood’s most famous studios, with its Leo the Lion logo and an almost century-long history.
The sale would give the technology giant’s Prime streaming service access to a vast back catalogue of iconic content.
Amazon and MGM Studios told the BBC that they did not comment on rumours or speculation.
The reports come just hours after telecoms giant AT&T agreed to combine its WarnerMedia unit with Discovery in a deal to create a new streaming giant.
MGM Holdings, the parent company of MGM Studios, has reportedly been exploring a sale since the end of last year, according to media reports.The purchase by Amazon of MGM Studios would mark a major step for its Prime streaming service.
MGM Studios has a huge catalogue of films and television shows covering the last ten decades, through the Golden Age of Hollywood to the present day.
In more recent times it has produced the James Bond movie franchise and The Handmaid’s Tale TV series.