New york: Serena Williams is poised to break Steffi Graf`s 25-year-old record for consecutive weeks at world number one but Angelique Kerber and Garbine Muguruza are relishing the opportunity to dethrone the queen of the sport.
American 34-year-old Williams`s latest spell on top of the pile started in February 2013.
That`s a stretch of 184 weeks which will become 186 during the US Open fortnight and match Graf`s mark set between 1987 and 1991.
Kerber, a German compatriot of Graf, had her chance to snatch top spot last week by winning the Cincinnati title but faltered in the final, a slip-up which kept her at number two heading into New York.
"I love the question (of the number one ranking). I love it," said the 28-year-old Kerber, who defeated Williams in the Australian Open final in January for her maiden Grand Slam title.
"Let`s see what happens in the next two weeks."
Kerber is right to be cautious having suffered in the past for allowing herself to get tied up in knots by predictions and permutations.
Last year at the WTA Championships in Singapore, she needed to take just one set off Lucie Safarova to make the semi-finals of the lucrative season-ender.
Instead, she got so distracted by the "ifs", "whats" and "maybes" that she was defeated in straight sets and was eliminated.
"I will not put too much pressure on this. If the day will come when I reach No. 1, that would be amazing," said the German.
"I learned a lot of things the last year, especially with the Singapore thing. So I will try to enjoy every moment right now because it`s one of the best seasons of my career."
Muguruza, the world number three, has an outside chance of taking the top spot.
But the 22-year-old Spaniard, who made her Grand Slam breakthrough with this year`s French Open title by defeating Williams in the final, has time on her side.
She is 12 years younger than Williams. When the American first made number one back in 2002, Muguruza was just eight.
"I feel the discussion (over the world number one ranking) is much louder," said the Venezuelan-born player.
"There are a couple of players that if they do really well and whatever the situations are, they can reach No. 1. So that creates a little bit of juicy comment."
The discussion is louder also because of the calibre of the players involved -- both Kerber and Muguruza are Slam winners.
Over the last decade, however, there were a series of women who reached the number one ranking without winning a major either at the time or since.
Jelena Jankovic (18 weeks in total in 2008 and 2009), Dinara Safina (26 weeks in two 2009 spells) and Caroline Wozniacki (two periods stretching over 2010/11 and 2011/12 totalled 67 weeks).
All three women made the finals at majors, went to number one but never cracked a Grand Slam title.
Jankovic was runner-up at the 2008 US Open, Safina made the finals of the 2008 Australian Open and 2008 and 2009 French Opens.
Wozniacki was twice a finalist in New York -- in 2009 and 2014.
Six defeats in total -- Williams was responsible for three of them.