The couple, who have been married for five years, separated in April and reportedly transferred their ex-wife, Charlotte Bernard, their two children and their mother from New York to their home in Bridgehampton soon after.
Olivier is said to be concerned about the coronavirus epidemic and wanted to protect them.
Mary-Kate, 33, filed for divorce from her husband, 51, this week.
A source told Page Six: “Olivier was concerned for the safety of his family in New York during the pandemic.
“He insisted with Mary-Kate that he wanted to bring his ex-wife, their children and his mother from the city home to Bridgehampton. “
The source added: “By the time MK came out of the aisle in April, Olivier had his mother, his children, and wait for that … Charlotte, his ex-wife, moved to keep them in a safer place, far from COVID. “
Mirror Online contacted representatives of Mary-Kate and Olivier for comments.
Mary-Kate was finally able to file for divorce this week after the New York courts were reopened.
Previously, she had tried to obtain an emergency order to end the marriage when Sarkozy had tried to drive her out of their apartment.
Reports suggest that he had terminated the lease on the house they shared.
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She allegedly claimed that the May 18 release date had not left her enough time to find her own accommodation.
The Full House star is said to have asked the lawyers for an extension.
The former couple started dating in 2012 and then linked in 2015.