The Bosnian feels Willian and Gary Cahill would be well-suited to represent the West London club in the 100metre sprint and dressage respectively.
He also named John Mikel Obi for the longer 1500m foot race and Nemanja Matic for swimming.
Begovic was asked these questions by the Chelseaofficial website in an Olympic-themed interview.
When asked who would he choose among his teammates to represent the club at 100m, he said: "We have a lot of fast players! I'd probably go Willian."
For 1500m, he said: "Who's a steady Eddie? Maybe John Mikel Obi", and for dressage, Cahill earned his vote because of his gracefulness: "That's a tough call. Maybe someone like Gary Cahill, a tall guy. A good physique is important."