After guiding Porto to a famous treble last season, 34-year-old Villas-Boas replaced Carlo Ancelotti at the helm of the Stamford Bridge side during the summer, and was being touted as the 'new Jose Mourinho'.
However, the Blues have failed to gain any consistency throughout the season and face a battle to qualify for a Champions League spot after losing their sixth league of the season at Everton on Saturday to slip out of the top four.
But Grant, who has recently taken charge of Serbian club FK Partizan, believes Villas-Boas is still learning his trade at a top club and deserves more time in order to bring success back to Stamford Bridge.
"When you sign a young coach, you have to give him some time," he told Yahoo!
"He will do good things if he is given time to show what he knows.
"One of the things I learned at Chelsea is that you have to handle things that go on off the park. It is not just a football club.
"Villas-Boas is a very nice guy and did good things at Porto, but he needs time."
The Israeli took Chelsea to the Champions League final in 2008, losing to Manchester United on penalties, and spoke highly of his predecessor Mourinho, with speculation linking the 'Special One' with a return to West London.
"Mourinho brings Mourinho to a club. He is a good manager, and has many great attributes," he added.
"The manager is like a director of the club. Off the park, he is a good guy.
"I spent three months working with him at Chelsea which I enjoyed."
For more insight from Avram Grant and other leading managers, plus exclusive Premier League highlights, visit www.yahoo.co.uk/sport
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