In recent months, King has kept an open mind about whether the WTA Finals should be staged in Saudi Arabia.
The decision to hold the year-end tournament in Riyadh was criticised by some because of the country’s human rights record.
Homosexuality is illegal in Saudi Arabia, while Amnesty International has cited the country’s “jailing of women’s rights activists, suppression of free speech and rampant use of the death penalty”.
Martina Navratilova and Chris Evert considered the awarding of the Finals to Riyadh for a three-year term to be a “step backward” for women’s tennis, but King, who is gay, argued it was important at least to engage with the Saudi authorities.
And now the first edition of the tournament has been completed, King says it is time for the WTA Tour and the players to decide if this should be a long-term arrangement.
“I think they have to decide. I know they [the Saudi Federation] did a lot of programmes. Let’s see if they stay, let’s see what happens.
“It’s a really hard one. For the girls that live there, I want them to see the best too. I would love to see a female player come out of the Middle East as the number one in the world as she could influence in a huge way I think.”