Juve's general director Giuseppe Marotta confirmed last month the club turned down an offer for Sandro from the Premier League champions, who were reportedly willing to pay up to €60 million.
Former Juve boss Antonio Conte, who is now in charge at Stamford Bridge, has been linked with a fresh bid for the 26-year-old left-back, who scored three Serie A goals last season as Allegri's men won the title for the sixth year in a row.
But Juve coach Allegri is determined to hold on to Sandro, having already allowed one of his defenders, Leonardo Bonucci, to join AC Milan in a surprise deal worth €42m.
"Alex Sandro? He's a Juventus player, he's extraordinary and he won't leave us," he told Premium Sport.
"He's improved so much since he came to Juve and he has the margins to improve again. Along with [Real Madrid left-back] Marcelo, he's the best in the world."
Juve have dominated Serie A recently, winning six titles in a row, but Allegri expects there to be a wide-open race for the Scudetto when the new season gets under way on August 19, with the holders due to host Cagliari.
"This year will be much more difficult because all our rivals have strengthened," Allegri said. "It will be complicated and tricky to win the seventh consecutive league title, but this is our first goal of the season.