Roland Garros takes place from May 25th to June 8th with Wimbledon then kicking off on June 23rd.
According to the Times respected tennis correspondent Neil Harman, Robson "has been advised that she needs an injection in the wrist, which will require a period of six weeks without competition.
"If the outcome is positive, she could be back on the court by early June; if not, an operation could be the answer, meaning that she would miss the entire summer."
Robson had hoped to return to action next week for the WTA Marrakech event but has been forced to withdraw from that tournament and the Madrid Open in early May.
She is still scheduled to play in the WTA Rome event from May 12 which would give her just one week of clay court action before the French Open.
Robson did climb as high as number 27 in the world last summer, but her persistent wrist problem has seen her drop to number 64.
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