Serena Williams says she’d love to eclipse Steffi Graf’s record 22 career majors at the Australian Open as she marches relentlessly towards a fabled calendar-year grand slam sweep.

Williams’ gritty French Open final triumph over Lucie Safarova followed her sixth success in Melbourne in January and has the American halfway to a grand slam, the one feat still eluding the all-conquering world No.1.

But already boasting five Wimbledon trophies and six US Open crowns, the 33-year-old is a hot favourite to emulate Graf’s 1988 feat of winning all four majors in the same year.

Such a scenario would leave Williams with the chance to top Graf’s open-era benchmark for the most grand slams when she arrives in Melbourne for her latest Australian Open defence next January.

“That would be exciting. I love Melbourne. I just can’t wait to get there,” Williams said after overcoming the flu and a Safarova fightback to land her third title in Paris with a 6-3 6-7 (2-7) 6-2 win over the Czech.

But it’s one step at a time for Williams, who held all four grand slam titles simultaneously in 2002 following her first triumph at Roland Garros and ranks that accomplishment among her greatest achievements in a truly remarkable career.

“I think you guys are forgetting that I have won the last three grand slams. You’ve got to keep focusing on this calender thing,” she said.

“So I would never have expected at this time in my career to win three grand slams in a row and no matter what happens at Wimbledon this, for me, is unbelievable.

“I’m really excited to have done this. I feel good about it.

“(I’m) three quarters of the way to a `Serena slam’. I don’t know if it will be more special if I make a grand slam.

“I think it will be awesome but, at the end of the day, it’s pretty awesome to have 20.”

Australians Rod Laver in 1969 and Margaret Smith Court in 1970 are the only players other than Graf since tennis turned professional 47 years ago to win all four grand slam singles title in the same year.

Smith Court retains the all-time record for most grand slam singles titles with 24.

But that is suddenly also now within Williams’ reach with the American having racked up seven almost in a blur since 2012 after suffering a life-threatening pulmonary embolism.

“I really didn’t think I could win another grand slam,” Williams said of her brush with mortality.

“So here I am at 20. It seems a little bit like a dream. Like, is this really my life? Is this really happening right now?

“It’s really kind of weird.”