Cavendish has famously missed out on medals in the last two Olympics; he placed ninth Madison alongside Sir Bradley Wiggins eight years ago in Beijing, and then 29th in the London 2012 road race around the capital and Surrey.
The 31-year-old is seeking to win gold in the omnium, which begins with the scratch race inside the Velódromo Municipal do Rio on Sunday, 14 August, and British Cycling's former performance director feels he is worthy of a podium finish.
“Cav deserves a medal,” said Brailsford. “We went to Beijing and it didn't work out, he put everything into that. We came to London, it didn't work out there either.
“Yet he's brave enough – and he is brave to do it, because he doesn't need to – to say I'm going to put my neck on the line again in an other Olympic games.
“After the Tour [de France] he's just had, I hope he really gets what he deserves.”
Cavendish placed sixth in the discipline at the Track World Championships in London earlier this year, but was within 30 points of victor Fernando Gaviria, his former Etixx-Quick Step teammate.
Gaviria (Colombia) beat the likes of Roger Kluge (Germany), Glenn O'Shea (Australia) and Team Sky's Italian rider Elia Viviani to the world title this March, all of whom will be competing for Olympic glory in Rio.
However, when asked if he backs Cavendish in the event, Brailsford added: “I do, actually. The field is the field, hopefully the best man wins, and it'll be really interesting to watch.
“Cav will have learned from the Worlds, that was the whole point of him doing it. He's fitter now, I think he's in better shape.
“You've always got to be cautious to compare the Olympics to the previous Worlds, they don't often go to form.
“The gap between the Worlds and the Games is a tricky length, six months or so. You can't sustain that form, you have to dip.
“People try and do it different ways, and British Cycling have done it right many times over the years. I think some teams have tried to stay on it too much, without naming names.”
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