Briton Froome, 32, sealed his fourth title and third in succession on Sunday's final stage in Paris.
The record for most Tour titles won is five, held by Jacques Anquetil, Eddy Merckx, Bernard Hinault and Miguel Indurain.
"Chris can go on - there's no reason to think that he can't," said Brailsford.
"Physically he's got what it takes and I don't think that's going to diminish in the next year or so."
Brailsford added that Froome's chances of winning more Tour titles were a question of "hunger and mentality" and that the Team Sky rider was "as hungry as ever".
"He's getting better tactically and technically, so as long as that hunger continues and he keeps his health, then he'll be a force in this race for a good couple of seasons to come," Brailsford told ITV4.