Froome believes Quintana has bitten off more than he can chew by aiming for the Giro d'Italia-Tour double and failing.
"I think it is going to be tough for Nairo to do the Giro and the Tour," he told Reuters.
The Brit however tipped former Australian team mate Porte as a major contender.
"Richie has been amazing this season, winning the Tour Down Under and recently the Tour of Romandie. I think this year's Tour suits Richie really well," he said.
Porte served as Froome's lieutenant at Sky from 2012-15 before leaving for BMC to become a team leader.
"He's definitely got a chance to be up there for the win. This season he has been showing what he is capable of. I always believe in Richie," Froome added.
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Porte primed for Dauphine
As for Quintana, the Colombian appeared to struggle during the Giro d'Italia's mountain stages and could not crack Dumoulin.
Although he did not see a lot of the race as he was in Tenerife for a training camp and there was no TV, Froome said Quintana could have been cycling within himself in Italy.
"He may then be doing better on the Tour because he is a rider who is better in the second than the first grand tour," the Kenya-born 32-year-old said.
"My biggest threats come from guys who did not do the Giro -- Richie Porte, (two-time winner) Alberto Contador and (last year's runner-up) Romain Bardet," Froome told Reuters.
Froome will once again rely on Geraint Thomas, who should be in good form for the Tour after his own Giro ambitions were dashed after his crash on stage 9 forced him to abandon the race.
"On the one hand, it was a huge setback for Geraint that he was not able to finish the Giro... but for the Tour, it will be only a good thing for the team because he will be fresher and have more time to prepare," Froome said.
Froome returns to racing this Sunday for the eight stage Critérium du Dauphiné. It will be the first time he comes to the race without a win to his name since becoming a serious general classification contender. But he doesn't see this as an issue.
"I think it has been a build up similar to what I had last year. I think it worked well and I was able to do the Tour and the Vuelta (a Espana).
"After the Tour, if everything goes well, I'd love to do the Vuelta," he added of a race he has finished runner-up three times.
Froome also dismissed the scrutiny of Sky by British politicians looking into the circumstances around a medication filled jiffy bag delivered to 2012 Tour winner Bradley Wiggins at a race a year earlier.
"It does not really affect much of us on the road," Froome said of his former team mate.
"It is different for Bradley and others who are no longer on the team, but for us it's really not a big deal, none of us have been involved in this."
Team Sky's roster for the Critérium du Dauphiné:
The Criterium du #Dauphine is just days away. Three-time race winner @chrisfroome leads our team in France. Check out our full lineup pic.twitter.com/31EiaHv23w — Team Sky 🚲 (@TeamSky) June 1, 2017
Sky reveals new kit for the Tour de France
We’re delighted to reveal our special white jersey edition of our @CastelliCycling kit for the Tour de France! 📝 > https://t.co/2jvYrpcSvq pic.twitter.com/IQ0kIP6qwR — Team Sky 🚲 (@TeamSky) June 1, 2017
Meanwhile, Sky has revealed a special edition jersey for this year's Tour de France.
Sky's gone for the cooler white option, rather than its traditional black but the Castelli jersey will still carry its distinctive data pattern design.
Sky are also offering fans the opportunity to see their names printed onto the blue line on the back of the jerseys and can enter .
