Anigo has been at the helm since Elie Baup's departure in December and is set to be replaced by former Athletic Bilbao boss Bielsa.
The Argentinean was present for the 3-2 victory over Montpellier last week and Anigo expects the 58-year-old to be appointed after he has finished taking stock of the club.
"I'm sure his response will be positive. He stayed here quite some time to see everything and people of that calibre analyse everything and take their time to give an answer. This is normal," he said.
"(He is) a man who has the charisma needed to manage a club like ours."
The victory in Montpellier kept Marseille sixth and in with an outside chance of European football next term.
Marseille have only lost four times in the league since the turn of the year and Anigo was left unhappy with suggestions that last Friday's win came as a result of Bielsa watching on.
"He was present in Montpellier but it did not bother me. Instead, he needs to see with his own eyes the players and the collective," Anigo continued.
"What bothers me, however, is the interpretation that people make - that players were more motivated because Bielsa was in the stands.
"It's not very respectful to us and it is simplistic with respect to our work."
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