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The 36-year-old, who has made just one appearance at Roland Garros since reaching the semi-finals in 2017, last month said he wanted another chance to play at the clay court Grand Slam while he is still fit and healthy.
Three-times Grand Slam champion Murray won the second-tier Aix-en-Provence Challenger Tour crown earlier this month, but suffered early exits in Monte Carlo, Madrid, Rome and Bordeaux.
The Scot has opted to skip tournaments during the claycourt season in the past to focus on the grasscourt swing heading into Wimbledon.
Reuters has contacted the French Tennis Federation (FFT) for comment.
The French Open runs from May 28 to June 11. Holder Rafa Nadal, who has won the French Open a record 14 times, also pulled out of the tournament after failing to regain full fitness from a hip injury.
