News of their impending parenthood broke only last December, when Hanna Prater - rarely seen in the F1 paddock - was reportedly eight months pregnant.
The birth of their child in a Swiss hospital caused a stir among his fans, but the famously-private Vettel has neither a Facebook page nor a Twitter profile, and so he could not confirm the news via social media.
And now Bild newspaper reports that the 26-year-old's management declined to confirm or deny the reports about Vettel's fatherhood.
What is clearer is that the Red Bull driver will have a new physical trainer in 2014, after working with Finn Heikki Huovinen in 2012 and 2013.
Before that, Vettel's well-known trainer was Tommi Parmakoski, another Finn.
And Sport Bild reports that Vettel's new trainer is yet another Finn, Antti Kontsas, who formerly worked with Toro Rosso driver Jean-Eric Vergne, and Red Bull reserve Sebastien Buemi.
All three Finns - Parmakoski, Huovinen and Kontsas - have links to the former McLaren doctor Aki Hintsa, who is close to Vettel.