"That's what we are discussing at the moment, to try to see if we can find this ideal scenario for Rio.
"It's doable, that's for sure," Brailsford told the BBC.
Wiggins signed for Team Sky in 2010 but has yet to agree a new contract after Brailsford left him out of this year's Tour de France line-up.
Wiggins won a silver medal on the track at the Commonwealth Games in Glasgow on Thursday before saying he was done with road racing.
"I've bled it dry," the 34-year-old said.
The Commonwealth silver was the latest prize in a career that has brought the Englishman four Olympic golds and the historic 2012 Tour de France victory, the first by a Briton in the sport's most prestigious race.
After losing out on gold to Australia in Glasgow, he said road racing was "quite cut-throat" and "political".
"The track feels more like a family and a closer-knit group of people," he said.
Responding to the comments, Brailsford said Wiggins was "entitled to his opinion".
He also defended Team Sky's competitiveness and Wiggins's claim that they were only interested in Grand Tours by saying most teams were just as focused on winning the big races.
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- Tour de France
- Commonwealth Games
- Team Sky