The Blues have been heavily linked with a move to sign the Brazil international but have struggled to reach an agreement with the Serie A giants.
Chelsea are thought to have made a number of offers to sign the South American defender as Antonio Conte looks to bolster his left-back options.
Sandro has impressed during his two-season stint in Turin after Juventus signed the left-back from Portuguese giants FC Porto in 2015.
Conte wants the Premier League champions to make Sandro their marquee signing of the summer despite making four new additions in recent weeks.
Speaking at a media conference in the United States about Chelsea’s interest in Sandro, Allegri was adamant that the 26-year-old wing-back will not be sold.
“Alex Sandro is a Juve player,” Allegri said. “He is sensational and will not leave.”
Chelsea started their summer transfer activity with the recruitment of Manchester City reserve goalkeeper Willy Caballero.
The Blues have also signed AS Roma defender Antonio Rudiger, AS Monaco midfielder Tiemoue Bakayoko and Real Madrid striker Alvaro Morata.
– Alex Sandro moved to Portuguese giants FC Porto in 2011 and won two top-flight titles with the club.
– The 26-year-old moved to Serie A champions Juventus in a €26m deal in 2015 following his impressive spell in Portugal.
– Sandro has scored five goals in 75 games in all competitions in his first two seasons at the Turin club.
– The Brazilian defender has already won two Serie A titles and the Coppa Italia twice but was part of the Juventus team that lost 4-1 to Real Madrid in the Champions League final.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news