Franz Tost is not sure there is reason for great optimism even though moves are being made to organise the first actual races of 2020.
Another Red Bull official, Dr Helmut Marko, said the chances are "very good" that the Austrian authorities will green-light the plan for races at the Red Bull Ring in July.
Silverstone also wants to be among the very first races in the summer, but circuit boss Stuart Pringle admits the decision will ultimately be the government's.
"We need to go back to the government in the next ten days and give them the detail of what the plan looks like," he said.
Amid a global shutdown that is struggling to be eased, Alpha Tauri boss Tost is not so sure F1's plans will work out.
"Logistically, Formula 1 is a large and difficult ship to steer," he told Speed Week.
"We currently have more questions than answers because so much is uncertain. Firstly, we do not know what individual governments will decide.
"We can outline what a return to sport looks like roughly, but we simply don't know whether it can all be done in the end," Tost added.
For instance, Marko acknowledged that F1 will need to do coronavirus testing at the first races, but Tost warned: "You have to be careful with these tests because there are now a lot of different ones.
"The whole situation is extremely complicated because we are dependent on government decisions and because so many individual factors all play a role.
"Of course the FIA and FOM would like to get started as soon as possible, but you have to know that these are only the desired scenarios.
"Perhaps we will be lucky with Austria in that the situation has developed in such a way that the government allows more freedom. The opposite could happen to us in England. We just don't know," he added.
