The Italian team was not immediately available to comment.
Germany’s best-selling tabloid, Bild and Auto Motor und Sport, both said the 32-year-old, who will be without a contract at the end of 2020, had rejected the terms proposed in a new deal.
They said the separation from Ferrari, the sport’s oldest and most successful team, could be officially announced on Tuesday.
The Italian newspaper Gazetta dello Sport recently announced that Vettel was offered a one-year extension with a pay cut.
Vettel joined Ferrari in 2015 after winning all of his titles with Red Bull and dreaming of emulating his childhood hero Michael Schumacher, who won five of his seven titles with the Maranello-based team.
The father of three told reporters last month that he could have a new deal signed before the start of a season delayed by the COVID-19 pandemic.
Ferrari has said the German is their first choice to team up with Charles Leclerc, but reports in Italy have said they want a response by the end of April to ensure that potential replacements are still available.
Leclerc, who won two races last year and is only 22, has a contract until 2024 and is considered the future future of Ferrari and probably the first champion since Kimi Raikkonen in 2007.
The Monegasque surpassed Vettel in his first season at Ferrari last year, finishing ahead of him in the general classification and obtaining more points, poles, podiums and victories.
Australian Daniel Ricciardo of Renault and Spaniard Carlos Sainz of McLaren have both been mentioned in the media as the main contenders for one of the most coveted seats on the grid. The two are also at the end of the contract at the end of 2020.
Lewis Hamilton, a six-time world champion, has also been linked to Ferrari, but has repeatedly stated that he intends to stay with Mercedes.
Formula 1 has postponed to 2022 a major technical rule change planned for 2021, which means that the teams will use the same cars next year.
Ferrari appeared to be behind Mercedes on pace during pre-season testing, but was unable to operate its car under race conditions due to the cancellation of the tournament opening on March 15 in Australia.
Sport hopes to get behind closed doors in Austria in July