Australia's newly crowned French Open champion returns to the court in Birmingham on Monday with a serious chance of seizing the top ranking even before Wimbledon.

After Birmingham, where she was a finalist two years ago, Barty will round out her Wimbledon preparations at Eastbourne.

Depending on how Naomi Osaka fares in Birmingham, the world No.1's only scheduled event before the grass-court grand slam gets underway on July 1, Barty could arrive at The All England Club with the top ranking if she wins one of the next two tournaments.

Barty admits it would be a surreal to become Australia's first women's world No.1 since her Indigenous idol and mentor Evonne Goolagong Cawley in May 1976.

"Obviously that's the next point, the next goal, the next situation I can see myself in," the 23-year-old said following her rise to No.2 after her Roland Garros breakthrough.

"Being No.2 in the world is incredible and something I never dreamt of as a child and we'll keep chipping away and try our best to get to No.1."

Barty dropped considerable rankings points after opting to withdraw from this week's WTA event in Nottingham, where she would have been defending champion.

Molik believes the sacrifice was further evidence of the former Wimbledon junior champion's maturity.

"I'm not surprised she's downed racquets. It's brilliant," Molik told AAP.

"It's reflective of the person she is; totally professional and she wants to rest her body because it could be another intensive three or four weeks ahead with Eastbourne, Wimbledon - and it's all pressure."

While Barty is seen as one of the Wimbledon favourites, Molik believes a run to the second week would be a success.

"She'll be approaching it wanting to get down to the last couple of players, but anything better than last year (when she made the third round) but there's so much pressure.

"Any improvement on last year would be a bonus and that would really set her up for the second half of the year and the hard courts."

Regardless of if and when Barty reaches the summit, Australia's first grand slam singles champion since Samantha Stosur won the 2011 US Open is predicting a long rivalry with 21-year-old Osaka.

"Obviously Naomi has been extremely dominant over the last period of time," Barty said.

"Last six or 12 months, she's had an amazing run. She's No.1 in the world for a reason. She's had an incredible run of tournaments and is playing some amazing tennis.

"We have only played a couple of times, but I'm sure that we'll play many more times over both of our careers, and hopefully they're in big matches."

Australian Associated Press