Anigo was appointed until the the winter break - a four-game stint - when Elie Baup was sacked at the weekend and kicked off his tenure with a hard-fought 2-1 defeat by Borussia Dortmund in the Champions League.
He tackles Ligue 1 opposition for the first time on Sunday when OM travel to mid-table Lyon and while Anigo insists he currently sees the job as a short-term fix the possibility of staying is not off the agenda.
"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."
Table-topping Paris St Germain were also in Champions League action in midweek, losing 2-1 at Benfica having already qualified as group winners.
Coach Laurent Blanc rotated his squad for the match but was still upset to lose the tie and wants a strong end to the year, starting at Rennes on Saturday.
"Even though I left some first-team regulars in Paris, my starting line-up still had a lot of internationals, we're disappointed but we need to move on," he said.
"Let's not forget that we had already qualified. Now we'll wait for the draw, which will play a big role in how far we can go in the Champions League, and focus on the last two league matches of the year as well as our Coupe de la Ligue clash with St Etienne."
PSG kick off at 4pm, three hours before the rest of the day's fixtures, meaning victory would, temporarily at least, take them five points clear of second-placed Monaco, who take on Guingamp at 7pm.
Claudio Ranieri's title hopefuls go into the game in good spirits with four consecutive victories and a clear midweek to recharge their batteries.
The opening match of the round sees Montpellier take on St Etienne on Friday evening, with Saturday's fixtures completed by bottom club Sochaux's trip to Nice, Nantes versus Toulouse, Evians against Reims and Ajaccio's home match against Lorient.
On Sunday, third-placed Lille host Bastia and strugglers Valenciennes go to Bordeaux.