Goal understands the left-back was keen to team up with then-Blues boss Antonio Conte with a €70 million (£62m/$80m) offer on the table.
Sandro remained in Turin, however, with Juve having already let Dani Alves and Leonardo Bonucci leave for Paris Saint-Germain and Milan respectively.
But the 27-year-old has now aired his ambition to test himself in England before the end of his career.
Speaking at a press conference while representing Brazil on international duty, he said: "I think, one day, who knows what will happen?
"I have a desire to play in the Premier League but right now I am very happy where I am at, the club I am at [Juventus], the league I am playing in.
"So today my only thought is to continue where I am because that's where I feel happy."
Sandro has registered two assists in Serie A so far this season with Juve leading the way at the top of the standings.
Massimiliano Allegri's men are unbeaten in their opening 12 league games, winning 11 and drawing just one.
Juve are also top of their Champions League group, having won three and lost one of their four Group H matches to date.