The 30-year-old has not won Olympic gold, having fallen short at the 2008 and 2012 Games.
He hopes to compete in the multi-event omnium in Rio.
"If he can't make the top three, he would pursue his dreams of the Tour de France yellow jersey," said Sutton.
"I believe he can do it, we wouldn't have selected him otherwise. That's not us being brutal, that's Cav being Cav, probably the greatest road sprinter of all time. He needs to know he can go to Rio and get the medal."
Cavendish has had a successful road season to date, having won the Tour of Qatar.
He is aiming to compete at the Tour de France, although men's endurance coach Heiko Salzwedel believes the Isle of Man rider will have to prioritise.
"If you ask me realistically, riding for two or three weeks on the Tour de France, he might be fit for the [Olympic] road race but not for the Olympic omnium," he said.
"Cav has to digest and make a decision about this
Cavendish will also compete in the madison - a non-Olympic event - with Sir Bradley Wiggins at the World Championships, being held in London early next month. They combined to win the title eight years ago.

They will be joined at next year's Olympics by South Africa who defeated Equatorial Guinea in Bata 1-0.
It is the first time that any Zimbabwe team has qualified for a global football tournament.
Rudo Neshamba's 8th minute goal was enough to send Zimbabwe to Brazil.
It's a great achievement for us, I'm so happy I can't even explain how I'm feeling right now
The result meant the tie finished level at 2-2 on aggregate, with Zimbabwe qualifying on the away-goals rule.
It was disappointment for Cameroon who represented Africa at the Women's World Cup in Canada, reaching the second round.
Neshamba (pictured) was again Zimbabwe's match-winner, having scored their crucial away-goal in the first leg in Yaounde.
Her captain, Felistas Muzongondi, said it was a famous day in their footballing history.
"It's a great achievement for us, I'm so happy I can't even explain how I'm feeling right now," Muzongondi told BBC Sport.
"This is our first time in history to beat Cameroon, and we were expecting this because we prepared very well."
Zimbabwe's skipper also admitted it was a very tough match.
"There was so much intensity so we had to put much pressure on them because they have so much more physical fitness than us."
Zimbabwe booked their place in Rio despite severe financial difficulties facing football in their country.
They were only able to continue in this qualifying tournament after Ivory Coast withdrew.
Also on Sunday, South Africa defeated Equatorial Guinea 1-0 in Bata to win the tie by the same score on aggregate after the first leg had ended goal-less.
Jermaine Seoposenwe's second half goal proved crucial for Banyana Banyana and was enough to win them their place in Rio.
The South African Football Association (Safa) President, Dr Danny Jordaan congratulated Banyana Banyana for their achievement.
"Today is a historic day for women football; not only have they qualified for the Rio Olympics but have done so in style - winning away from home in 'hostile' Bata environment," Jordaan said in a statement.
"Few teams survive trips to Equatorial Guinea as Nigeria would attest but coach Vera Pauw plotted one of the greatest wins in South African football history," Jordaan added.
South Africa's progress to the Olympics makes up for their disappointment of missing out on qualification for the Women's World Cup earlier this year.
Mark Cavendish must finish in the omnium top three at the Track Cycling World Championships to have a chance of competing at the Olympics, says British Cycling technical chief Shane Sutton.
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Zimbabwe's women beat Cameroon 1-0 in the second leg of their final Olympic qualifier in Harare to book a place at Rio 2016.