Having climbed to a career-high ranking of second on Monday, Tunisian trailblazer Ons Jabeur was already plotting on dethroning Iga Swiatek as the world number one.

The 27-year-old surpassed South African Amanda Coetzer -- who reached the world number three ranking in 1997 -- to become the highest-ranked African player in history.

But Jabeur is aiming higher.

"I do feel more confident. I do feel like I deserve to be in this level. Hopefully, next step will be number one," Jabeur told reporters after storming into the Wimbledon second round with a straight-sets win over Swedish qualifier Mirjam Bjorklund.

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"It's going to be tough, but not impossible. Obviously, Iga is kind of a little bit far from us now... I'll try my best to catch up to her. Obviously if I don't do it this year, hopefully beginning of next year.

"But the most important thing, I want to have the level to be number one. Everybody is looking forward to win against number one. I want to be, like, really deserve that spot. Hopefully I can be the level that Iga is playing right now."

Jabeur was considered the most likely contender to beat Swiatek at Roland Garros, having arrived in Paris after winning a title in Madrid and a runner-up finish in Rome.

But she crashed out of the claycourt major in the opening round.

"I don't like to make the mistake twice," Jabeur, a Wimbledon quarterfinalist in 2021, said with a big smile. "I learned a lot from the first round in Roland Garros.

"Obviously, everything feels different here. I feel like more ready. Starting Monday not Sunday is much better for me. Let's say I opened the Court One, and it was great.

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"I enjoy playing a lot on grass. Scheduling, playing few matches, just get the perfect amount of playing on grass was great."

Jabeur lifted a grasscourt title in Berlin two weeks back and played doubles last week at Eastbourne with 23-times major winner Serena Williams.

"Gaining more confidence playing along Serena also helped me with the great attitude on the court," Jabeur said, adding that she was living the dream.

"Kind of start to be a leader on the court. That's what I'm trying to do. Trying to have that attitude."