Due to an unfavourable situation caused by coronavirus, and therefore the inability get together all my team, I made a difficult decision to refuse to participate in Cincinnati and the US Open.
The 35-year-old Kuznetsova beat compatriot Elena Dementieva in the 2004 US Open final to win the first of her two career Grand Slam titles.
"If there is a quarantine it will mean that players cannot play Madrid and Rome," Frenchman Mouratoglou told.
"But if they can't play Madrid and Rome and have to be quarantined that would mean they're sitting in an apartment for two weeks right before playing a Grand Slam on clay which sounds a bit crazy."