Allegri completed a fourth domestic double in as many seasons in Turin, with Sunday's goalless draw against Roma sealing a seventh straight Scudetto overall for the Bianconeri.
The 50-year-old has been touted as a frontrunner for the vacancy created by Arsene Wenger's departure from Arsenal but told a post-match news conference at the weekend that he would only leave the Allianz Stadium if the Juve board sacked him.
"We will have a discussion with him in the coming days, it also depends on his feeling and evaluations. On our part there is great optimism," he said.
"Beyond the formal aspect, the two-year contract that he still has with us, the assessment is that of a relationship that has worked at its fullest.
"The coach has proven his worth and I believe this relationship will continue."
The golden era overseen by Allegri was certainly not anticipated when he succeeded club great Antonio Conte in 2014, six months on from being sacked by AC Milan.
"We remember very well when he arrived, we were greeted by a hundred angry fans," Marotta recalled. "That was the climate of that time, tied to a bad appreciation of the facts.
"We were sure of our choice and solved a problem in that moment."
Marotta added: "Over the past 20 years the profile of the coach has changed. It is someone who should be good at managing the group and must be able to prepare the team, but also manage men and communicate with players. "