Gignac has been in fine form this season, scoring 10 goals to fire Marcelo Bielsa's side to the top of the table after 13 matches.
The striker picked up an ankle injury during training on Thursday and played no part in Friday's sessions ahead of this weekend's match at the Stade Velodrome.
The news came hours after coach Marcelo Bielsa had named the Cignac in his starting XI during a media conference on Friday, though he did admit they will have to monitor his progress.
"We'll see how the pain develops," he said. "If he is not ready in time Michy Batshuayi will take his place."
Alessandrini has also played an integral part in Marseille's rise this season, the attacking midfielder making 12 league appearances and scoring one goal.
However, he too remains a doubt to face fourth-placed Bordeaux, having also suffered an ankle injury.
The 25-year-old suffered a sprain to his left ankle and the club confirmed on Friday that he may miss Sunday's clash.
'I asked Cristiano Ronaldo, "Did you mean it?" He went, "Sorry?" I didn’t think he’d heard, but he had and was like, "Are you f**king kidding? Yes I meant it!”': When the Portuguese superstar didn't like being doubted
“I got knocked down by a big Irish striker after the first touch on my debut – I was lying on the floor, then Gus Poyet said, ‘Hey, welcome to British football!’”: Ex-Chelsea star recalls first Premier League encounter
