- I feel very, very close to Caroline. I just continue to be encouraging and I am overwhelmed by seeing what she does and continues to do, Williams tells Ekstra Bladet.

Williams has also had her challenges with illnesses, such as when she suffered blood clots in her lungs after giving birth to her daughter two years ago.

"I know all about these moments beyond the camera's spotlight, off the track, and I think she's so brave that she continues to do what she does at that level," says Williams.

Unlike Wozniacki, the American remains in the US Open and is set in the quarterfinals against Chinese Wang Qiang, who surprisingly knocked out second-seeded Ashleigh Barty.