Antonio Conte guided Chelsea to the Premier League title in his first season in England, but is yet to strengthen his squad ahead of the next campaign.
Sandro, capped seven times by Brazil, joined Juventus from Porto in August 2015 and has since won successive Serie A and Coppa Italia titles.
"We said no to a very good offer from Chelsea for Alex Sandro.
"But we know that we are competing with clubs that are in a position to offer wages that are not rational for us. And players are always their own boss.
"I do not know how Alex Sandro reacted."
Reports in the national press had suggested Conte had become frustrated with the Chelsea hierarchy over a lack of investment in the transfer market, but Sportmatch understands technical director Michael Emenalo and director Marina Granovskaia are aware of the Italian's targets and are continuing with their recruitment efforts.