Another calf injury prevented Carter from playing in the Top 14 last weekend.
The All Blacks great had only just returned from a month's absence the week before with critics suggesting he "lacked rhythm, accuracy and was very far from the flamboyant and precise starter that led the club to championship glory in 2016".
The 35-year-old has managed just three Top 14 games this season and Racing have already moved to bolster his position by signing Springboks star Pat Lambie.
When The Parisien asked Racing's Laurent Labit if Carter would sign on for another season, the assistant-coach was reticent: "He's thinking right now. We do not know yet. He will only do it if he is sure that his body is following."
Carter is in the final season of a three-year deal after he helped the All Blacks to consecutive World Cups in 2015.
Carter remains a favourite with his teammates who say his influence can't be measured in performance though they back him to bounce back from his latest struggles.
"He's a great professional, he's working hard and he's going to get his level back. He counts a lot for us, his presence reassures us in games but also in training," loose forward Antonie Claassen, a South African-bortn French international, said.
But the newspaper predicted that with Carter appearing unable to play week-in and week-out any longer, "he will not extend his contract".
Photo by: GETTY IMAGES (Caption: Dan Carter is reported to be weighing up his future at Racing 92 as injuries plague the final year of his contract)