The US Open is, for the moment, still on. And yet there is increasing pessimism within tennis that the tournament can survive the United States' escalating health crisis.

Cases in New York have fallen sharply since April, but concerns over quarantine - both on arrival, and when travelling on to Europe to prepare for the French Open - have not yet been allayed.

World number six Stefanos Tsitsipas could speak for many when he says: "I am 50:50."

"I personally would go and play, but if things get worse and our health is in danger, then the US Open and everyone involved should suspend the event for this year," the 21-year-old told Sportsworld on the BBC World Service.

"The mood has gone south in the last week or two," was the way someone else put it, with one agent no longer expecting the championships to go ahead.

The US Open is scheduled to be played behind closed doors in New York from 31 August, but if it is to be cancelled, the decision is likely to be taken by the end of this month.

The governor of New York State, Andrew Cuomo, invested a lot of political capital in giving the US Open the green light last month, but in recent days has had to introduce a 14-day quarantine for travellers arriving from no fewer than 19 US states.

Florida, which is either a home or a training base to so many professionals, is one of the states on the list. Will players be granted an exemption?

And how will the Spanish, Italian and French governments view the arrival of players and their entourages from New York for the delayed clay court season?

The European Union Council is still recommending a ban on non-essential travel from the United States. The advice will be updated every two weeks, although it is for member states to decide who should be exempt, and whether a period of self-isolation is required.

Jamie Murray has won the US Open mixed doubles title for the past three years, and admits staying in Europe to play "seems like a less stressful option right now".

"I think that will potentially come to a head soon with the ATP and US Open," he continued.

"And I'd imagine for the ATP, it would be very difficult to support the US Open going ahead if the draw has to quarantine coming back to Europe where they have two Masters Series and another Grand Slam.

"From my point of view as a player, you just want stability. Right now we don't have that. There have been a lot of things changing with not that fantastic communication I'd say."

There is also the issue of fairness. If the EU Council's advice is followed to the letter, then on the grounds of nationality, barely half of the women's top 40 will be free to travel to Palermo and Prague for the resumption of the WTA Tour.

Many are desperate to start playing again. The American number one John Isner has congratulated the US Tennis Association for their "forward thinking" in going ahead with the US Open, and Serena Williams committed to playing last month.

Overseas players have been more circumspect, or in Nick Kyrgios' case, scathing. "Selfish" and "stupid" is the Australian's take on the US Open proceeding as things stand.

Novak Djokovic - who has told Serbia's Sportski Zurnal he has been the target of a "witch-hunt" for his part in the ill-fated Adria Tour - says he is "not sure" whether he will play.

He has been more vocal in his opposition in the past, though, while Rafael Nadal - another to have expressed reservations - is officially keeping "all options open".

Both have said they will play in the Madrid Open the week after the US Open, with Djokovic making clear he wants to compete in Rome as well before the French Open gets under way on 27 September.

In some ways, though, the prospect of a US Open without Djokovic, Nadal and Roger Federer - who will not play again this year - is the least of the USTA's worries.

The organisation has had to cancel all five ITF World Tennis Tour events scheduled to take place in the US in August "to ensure the health and safety of all those involved".

There is still no word on the entry deadline, which - in a normal year - would be just 10 days away.

"I don't think we know from day to day if it's going to happen," the 18-time Grand Slam champion Chris Evert told Today on BBC Radio 4.

"I mean, right now in Florida, it's five times worse than it was two weeks ago."