That leaves Vettel now without a contract for next season, with the four-time champion's realistic options limited to Mercedes and Renault. "Looking forward, obviously I want to make sure I make the right decision for myself and my future".
"Well, at the moment I'm not really having any [plans]". I have a very competitive nature - I have achieved a lot in the sport, I'm motivated and willing to achieve more. I don't think that has anything to do with the fact that my contract expires and I am going to leave the team, but at the same time you are racing for yourself.
One possible option for Vettel is Renault, which is losing Daniel Ricciardo to McLaren next year, but Alonso is also being considered by the French team as his replacement.
"I think we decided to make a step back to try and analyse where the issue is coming from to then work on the issues, first to know exactly where it comes from, and that's where we're at for the moment, we have tried a different route for Budapest". You have to be aware of the decision you are making at the time, and that's also why I'm not rushing into anything.
Team-mate Sebastian Vettel said he was intrigued to know just where Ferrari will stack up this weekend after its disappointing showing in testing. The announcement stated Vettel and Ferrari had failed to reach an agreement to extend the partnership after team principal Mattia Binotto had previously called the German his first choice, but Vettel says there were never talks about an extension.
Vettel's Ferrari seat alongside Charles Leclerc will be taken in 2021 by McLaren's Carlos Sainz, whose position in turn will be filled by Daniel Ricciardo, now at Renault.
The increasing tensions between Vettel and Leclerc last season culminated in a crash at the Brazilian GP in November.
Charles Leclerc says he is "99 percent" sure that Ferrari is going to face a more hard Formula 1 campaign in 2020 than it had past year.
"But surely should the situation arise, it would make flawless sense [to] expect both drivers to help each other out".
The ongoing coronavirus pandemic is still creating uncertainty over how many races can actually be held - and where.
"I think at the moment we have eight races scheduled".
Not only were they already off the pace of Mercedes and Red Bull, but both their rivals have upgrades on their cars which will make them faster.
If the season continues beyond Europe, it will end with races in Bahrain and Abu Dhabi in December.
Confirming their first round of updates will instead appear at the season's third round - in Hungary in two weeks' time - Ferrari chief Mattia Binotto said their disappointing form in winter testing had led to a rethink with the SF1000. "It's an unprecedented scenario".