Vidal was a key member of the side that won three consecutive Serie A titles under the guidance of Antonio Conte.
However, the Chile midfielder has been linked with a move away from Juve, with Manchester United thought to heavily interested in taking Vidal to Old Trafford.
Juve's apparent willingness to part company with Vidal is believed to be among the reasons why Conte left the club on Tuesday and was swiftly replaced as coach by Massimiliano Allegri.
But, speaking at Allegri's introductory press conference, chief executive Marotta stressed that Juve have no desire to sell the 27-year-old.
"Vidal is not for sale, he is one of the most important players in the squad," Marotta said.
"Vidal is our player, big clubs asked for him but he'll stay and he's happy here. We've never put him up for sale."
Since joining Juve from Bayer Leverkusen, Vidal has scored 40 goals in 126 appearances for the Turin club.
