The 2016 world champion broke the news on Friday afternoon ahead of the FIA Prize giving ceremony in Vienna, saying he is keen to spend more time with his family after achieving his childhood dream of winning the title.
On the McLaren-Honda driver, Ecclestone told news agency Reuters: “It's possible I suppose, let's see. They've got new management now at McLaren. Maybe he's fed up being there and they're fed up having him.”
Long-time McLaren boss Ron Dennis was recently forced to step down from his role, with American motorsport marketing expert Zak Brown joining as executive director.
On the prospect of seeing Vettel team-up with Hamilton, Ecclestone was more unequivocal: “I think not. I don't think Seb would want to be with Lewis.”
Ecclestone adds that the “obvious answer” to replace Rosberg would be Red Bull ace Max Verstappen, though the 19-year-old is under contract until 2018.
Hamilton and Alonso have previous history as team-mates when the Briton took F1 by storm as a rookie in 2007 at McLaren.
The two drivers spectacularly fell out when the Spaniard felt the Woking-based team was leaning towards Hamilton and left McLaren after a single season.