The next round in the grudge match between world No.1 Serena Williams and Maria Sharapova has been booked at the Brisbane International.

The way Maria Sharapova sees it, there is no rivalry with world No.1 Serena Williams.

“I think I got to win a few times in order to call it a rivalry,” laughed Sharapova, who has lost her last 13 matches to Williams.

But it was clear her relationship with nemesis Williams was as frosty as ever after they booked a Brisbane International semi-final grudge match on Thursday.

Williams hinted on Thursday that Sharapova had crossed the line in their sometimes poisonous feud.

And Sharapova refused to backtrack on a recent newspaper article in which she confirmed she did not get on with the 17-time grand slam winner.

The next round between the pair will be in the Brisbane semi-finals after defending champion Williams thrashed Slovakian ninth seed Dominika Cibulkova 6-3 6-3.

In contrast, third seed Sharapova needed two hours to subdue Estonian Kaia Kanepi 4-6 6-3 6-2.

The stage is set for an intense semi-final after Williams on Thursday refused to comment on the incident that marked an all-time low in their conflict.

Sharapova surprised many ahead of Wimbledon 2013 when she responded to Williams’ magazine article comments which mocked an unnamed top five player – presumed to be the Russian – and said her boyfriend had a “black heart”.

Sharapova’s beau is world No.23 Grigor Dimitrov, reportedly Williams’ ex.

“Maybe she should talk about her relationship, and her boyfriend that was married, and is getting a divorce and has kids,” Sharapova said pre-Wimbledon, referring to Williams’ coach Patrick Mouratoglou.

Asked about the exchange on Thursday, Williams hinted that Sharapova had made it personal.

“I don’t think that question is for me. I didn’t go anywhere like that, so…,” Williams said.

“I had a great talk with her (Sharapova). For me, I don’t have anything against her or anything.”

Sharapova said she had no regrets over the recent New York Times article in which she confirmed her on-court respect for Williams but admitted their off-court relationship was “different”.

“That was one of the reasons why I wanted to do that interview. There were a lot of questions being asked and a lot of questions thrown in the air,” Sharapova said on Thursday.

“I thought it was really important to clear the air, and I think I said everything I had to say about it.”

Sharapova has a 2-14 record against Williams and has not won since 2004.

Her drought does not look like breaking based on Thursday’s evidence.

Sharapova made 33 unforced errors against Kanepi – 17 in the first set alone.

Williams was a picture of perfection, however – not conceding a first set service point for the first time since her junior days.

“I think she goes up and wants to play the best tennis against me,” Sharapova said.

“We’ve had pretty intense matches in our career.”

Fourth seed Jelena Jankovic has also reached the semi-finals after she defeated German Angelique Kerber in three sets.

The former world No.1 responded after dropping the opening set, beating fifth-seed Kerber 6-7 (8-10) 6-3 6-1 to move into the final four.

Jankovic will next meet world No.2 and defending Australian Open champion Victoria Azarenka after the second seed from Belarus overcame determined Swiss Stefanie Voegele in Thursday’s night match.

Azarenka won 6-4 6-7 (7-9) 6-1 but raised plenty of eyebrows after failing to close out the match in straight sets despite having eight match points in the second set.

The Belarusian will return to action on Friday afternoon with the semi-final against Jankovic before Williams and Sharapova meet in the evening session.