Dutchman Verstappen, 20, is regarded as a definite champion of the future, but he has been signed up by Red Bull through 2020.
Before that happened, Ferrari re-signed the Finnish veteran Kimi Raikkonen for 2018.
"I don't know what [Sergio] Marchionne will do, he is unpredictable," Briatore told Rai radio.
"But with Raikkonen you will never win the constructors' title. To win you need two good drivers, and Ferrari does not have that.
"I would sign Verstappen with my eyes closed. He is the only real driver that people want to see - a gladiator that they do everything to penalise in every race."
Briatore also hailed Lewis Hamilton's 2017 title triumph, saying: "This year he was more motivated on the track than in the disco."
Meanwhile, F1 legend Niki Lauda thinks that Ferrari president Marchionne was right to say that driver mistakes cost Ferrari the chance to beat Hamilton.
"I know Sergio well and like me he says what he thinks, although sometimes I'm a little more diplomatic," the Mercedes team chairman told La Gazzetta dello Sport.
"But I understand. They lost the championship - it's right to be critical."
The 2017 championship concludes next weekend with the Abu Dhabi Grand Prix.