The Ligue 1 outfit have been without a permanent boss since Elie Baup was relieved of his duties earlier this month, and were expected to make a new appointment over the Christmas period.
However, Anigo, who is also the club's sporting director, now claims that president Vincent Labrune will take his time over finding a replacement.
"The president spoke to me for a long time before the game (2-1 Coupe de la Ligue victory over Toulouse on Wednesday)," he said. "He's going to take his time to pick a new coach, it could take five months.
"I'm here till Christmas and I'll be here when we start again.
"I don't know what will happen after the season resumes. It wasn't what I had planned, but I'm at the service of the club.
"I expect the second half of the season to be difficult, but it's a great challenge."
Anigo has won one, drawn one and lost one of his three games in charge so far.
Marseille sit sixth in the French top flight, 15 points adrift of leaders Paris Saint-Germain.
‘Even though it was late in the game, the Arsenal fans started singing my name. It felt like the moment I announced myself as a professional footballer’: Ex-Gunners star recalls scoring first senior goal as a teenager at Highbury
'I started to drive myself crazy': Former Manchester United midfielder explains why it all went wrong for him under Erik ten Hag
