Wiggins, the 34-year-old quadruple Olympic gold medallist who became the first Briton to win the Tour in 2012, said on Friday the team would concentrate on delivering Kenyan-born Froome a second consecutive title.
But with the Tour due to start in Britain on July 5, Brailsford told Britain's Sunday Times newspaper that he would pick his nine-man team after this month's Criterium du Dauphine.
"Despite the impression that might have been created, the team for the Tour is not yet finalised," Brailsford said.
"I will be the one making the decision on who is in the team. I speak with our performance team, the riders can offer an opinion but they don't select the team and they never will."
With Froome selected to ride in the Dauphine, the traditional warm-up ahead of the Tour, Brailsford admitted the 29-year-old is in pole position to lead the team across France.
But Brailsford dispelled suggestions that Froome would have the final say on the selection of the team, especially given the fractious relationship between the two riders after Froome helped Wiggins win the 2012 Tour.
"Trust and harmony are important considerations and it is a difficult decision," he added. "I'm not just talking about the harmony between Chris and Brad but harmony amongst the riders and staff.
"People should be careful before thinking Chris is making decisions here. Chris is a great bike rider, he deserves to lead our team but ultimately he doesn't pick the team. I do."
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