Anigo took charge for the Ligue 1 club's 2-1 Champions League defeat to Borussia Dortmund on Wednesday following the sacking of Elie Baup.
The 52-year-old, who normally serves as Marseile's sporting director is set to take charge of the final three games before the mid-season break - though he has hinted he would be open to continuing in the role.
"I'm not quick to speculate about my own future - my mission is four matches, and three remain," he said.
"When doing this job, in this club, you cannot help but be affected: I've worked for this club for ten years, it gets better but it is also sobering.
"I'm not thinking of my project beyond January. I am not against continuing, if the president cannot find anyone who suits him.
"But once everything has been said the most important match happens against Olympique Lyonnais on Sunday."
Marseille sit fifth in Ligue 1 - 13 points behind leaders Paris Saint-Germain - and have won just one of their last five games in all competitions going into their trip to Lyon.