Anigo took charge for the Ligue 1 club's 2-1 UEFA 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, has coached the Provence club on an interim basis on a number of occasions.
And, while Anigo insists he is only focusing on Marseille's final three games before the mid-season break, the former defender is open to the idea of extending his spell as coach.
"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 in 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 Lyon on Sunday."
