James Lawton: Serena Williams tempted by battle of the sexes as latest challenger reduced to a shrug

'Andy Murray is one of the top three people I don't want to play but maybe we can...' says world No 1

Serena Williams runs for a return against France’s Caroline Garcia (AFP/Getty Images)

Caroline Garcia, a 19-year from Lyon, was playing the kind of tennis which persuaded Andy Murray that one day she will be the world's No 1.

Elegantly, she unfurled a series of shots which were laden with the clearest evidence of superior class. Her serve had bite and a velocity which consistently soared above the 100mph mark.

Then something quite brutal happened at the net that not only silenced the growing encouragement of the fans on Court One but also provoked a Gallic expression of despair worthy of the great mime artist Jacques Tati. It was easy enough to interpret because it asked the biggest question of all in women's tennis: how do you stop Serena Williams?

She came here in the deepest controversy, wrestling through disagreements with Maria Sharapova, issuing apologies, trying to hold her ground, but that seemed like old, extremely stale business. Garcia earned her respect – "she is a player of exceptional skill," said the winner of 16 Grand Slam titles – but the consequence was that piece of savage retaliation at the net. It was followed, immediately, by a screaming ace that registered 123mph.

She overwhelmed Garcia 6-3, 6-2 in barely an hour and came off court to be vastly entertained by the news that Murray was intrigued by the possibility of taking her on in one of those old-fashioned battles of the sexes in Las Vegas. This may have involved quite a lot of Scottish and American tongues in the cheek, but about one thing there could be no doubt.

At 31 Serena Williams is looking ever more the force of nature – and a strengthening favourite to pick up her 17th Grand Slam title a week tomorrow. She has her moods, her quite dramatic attitudes, but on the court her power and her genius for pushing aside all but the most essential business has rarely been so pronounced.

Garcia, a proud young lady, was at pains to explain her body language. She said: "It was not a gesture that said I could not find any solution to the problems of Serena. It just said it was so very, very hard. She is the greatest of players, of course.

"When Andy Murray said he thought I could be a No 1 it made me very proud, but it also reminded me of how much you have to do to get to the level of someone like Serena. Still, I agree it is a very good ambition."

Murray's interest in colliding with Williams on the court was most gently deflected. Williams said she remembered a little too vividly the defeats inflicted on her and her sister Venus by the gnarled old German pro Karsten Braasch at the Australian Open in 1998. The Williams girls started it, claiming that despite their tender ages – Venus was 17, Serena 16 – they could whip any man ranked lower than 200. Braasch responded with 6-2 and 6-1 wins over Venus and Serena respectively and then supplied another touch of topspin, saying: "I played like someone ranked 500 or so just to make it a bit more fun."

Serena plainly still feels somewhat chastened: "I don't know what would happen if I played Karsten today. I would probably still lose to Karsten. I was very young when I first played him and I'm a lot more experienced now. Andy is probably one of the top three people I don't want to play. But, yeah, maybe we can have a little bit of a showdown. That would be fine. I get the alleys and he doesn't get to serve. He gets no legs, either, he can't use his legs."

She was no doubt lifted by clear signs of progress in her latest Wimbledon crusade. "I'm still adjusting but I was pleased by my performance today. I have more work to do but I was encouraged because this was a player."

Murray was moved to predict a significant future for Garcia when he saw her take the first set off Sharapova in the French Open two years ago, then stroke her way to a 4-1 lead in the second. The Russian survived but not without obscuring the potential of a dangerous young talent.

A challenge of a quite different order faces Williams in the next round when she faces the Japanese veteran Kimiko Date-Krumm, who two years ago provided ferocious opposition for Venus. Even at 42, Kimiko has registered as a threat to Serena, who said: "Kimiko has great hand-eye coordination. She returns unbelievable shots. It doesn't matter how hard you hit it, she sees the ball and gets it back. She has great hands, has a wonderful volley, comes to the net a lot, which on grass can be tricky. She plays really flat, so the ball stays low.

"I did see that match she had with Venus. I think I lost four years of my life watching it. So I will definitely be talking to Venus and figuring out what I can do to do the best that I can."

She glows at recent praise from Boris Becker and Martina Navratilova, at the core of which is the belief that today's version would beat the Serena Williams of 10 years ago. "I think either way it would be a super tough match," she said, "but the big thing for me is that great champions are saying that I'm playing really well."

This is not to mention young Murray's idea of a girl who might just inherit her empire, the one who waved her arms at the heavens and said the woman across the net was just too strong.