The businessman of 80 years with two daughters, Petra, aged 22, and Tamara, aged 26, who would both be a couple.
Vettel for his part in a couple too, with his girlfriend the last few years, Hannah Prater, whom he met at school in Heppenheim.
Nevertheless, Ecclestone does not seem to Vettel if he longed to join the family.
"It would be an excellent step-son! It's funny, normal, its objectives and has worked hard to achieve. I really appreciate it very much.
"Same as it does not bother me at all . He should ask me, "laughed the boss of F1.
Moreover, Vettel said Sunday during a promotional event in Austria, he was very comfortable with Red Bull and had no intention of leaving the boat in the near future.
"I'm young and everything can change very quickly, but for now, there is not much to say about my future.
"I am contractually and personally happy and I am delighted that this will continue over the coming years," said the young champion.