The 26-year-old is in contention to qualify for the season-ending WTA Finals, which will be staged in Riyadh for the first time this November.
“I’ve been given guarantees that I’m going to be fine,” the world number 11 told BBC Sport when asked whether gay players should feel comfortable taking part.
When questioned at Wimbledon last year, Kasatkina expressed reservations about the Finals going to Saudi Arabia – saying there were “many issues concerning this country”.
But speaking at the Madrid Open after a third-round victory over Anastasia Pavlyuchenkova, Kasatkina spoke of the benefits of taking the tour’s flagship event to Riyadh on a three-year deal.
“If I qualify, it means that I am top eight in the world – it’s great news for me,” she said.
“We see that the Saudis now are very into the sport, they want to develop the sport. And as long as it gives the opportunity to the people there, and the young kids and the women to actually see the sport – so that they can watch it, they can play it, they can participate in this, I think it’s great.”
Human Rights Watch told the BBC in December that Saudi courts had convicted people for promoting homosexuality online and added “LGBT people in Saudi Arabia have to practise extreme self-censorship to survive their daily lives”.
In response, Arij Almutabagani – the president of the Saudi Tennis Federation – said gay players would not need to act any differently to the way they do in places like Abu Dhabi and Dubai, where WTA tournaments are already staged.
“People can behave the way they want to – there is nothing that says you can or you cannot behave. You just have to understand that every country has its rules and traditions,” she said.
“It’s the same thing that has happened in Dubai. How do they act in Dubai? We are the same, we are all neighbours. Saudi Arabia, Qatar, Kuwait, UAE – how would the players behave there?”
WTA chief executive Steve Simon has said representatives of the LGBTQ+ community were included on fact-finding trips to Saudi Arabia, before the deal for the WTA Finals was concluded.
Tunisia’s world number nine Ons Jabeur has also reiterated her support for the Saudi Finals.
“As an Arab woman, I’m very proud some things are moving there in Saudi,” she said in Madrid.
“Like Princess Reema said: you should come to Saudi, be there, and judge yourself.
“For me, it always has been about chances, and going there not just to play tennis matches but to give the opportunity especially for younger women to see their role models and to believe that they can achieve anything.”