The prestigious tournament is scheduled to begin at a behind-closed-doors Flushing Meadows on August 31, with the US Open organisers (USTA) creating a bio-secure 'bubble' in an attempt to ensure the safety of everyone involved.
However, while the spread of Covid-19 remains highly prevalent in the United States, there are significant concerns over facing mandatory quarantines following the players' returns home.
"I understand and respect all the efforts they are putting to make it happen in a safe environment, but I still don't feel comfortable to travel to US without putting my team and myself at high risk," last year's semi-finalist Svitolina said on Twitter.
Bertens wrote on Instagram: "The situation around COVID-19 is still worrying and the health of everyone and the control over this virus is priority.
"Our Prime Minister indicated yesterday that we should be quarantined for 14 days after coming back from the States.
"Of course we respect this as a team and this would disturb our preparation for my beloved clay court tournaments in Rome and Paris."
Meanwhile, former World No.1 Andy Murray, whose 2012 US Open win was the first of his three Grand Slam titles, will be in attendance having been handed a wildcard invitation to the tournament.
The Scot believes an opportunity to play is "worth the risk", but on Monday agreed players needed assurances they wouldn't subsequently have to quarantine.