By John Stonestreet

PARIS (Reuters) - As a serial winner Serena Williams has broken records without a backward glance throughout her career, but since September there is one milestone that has loomed ever larger in halting her progress toward the game's pantheon.

It is marked 'total grand slam wins', and frames a debate about who to consider the greatest woman player of all time.

One name on a very short list of candidates is Serena herself and another is Steffi Graf, who holds the professional-era record of 22 singles titles at the game's four blue riband events.

The American is one behind that and, back in September when she seemed as dominant as at any time since turning professional in 1995, looked odds-on to tie the record at the U.S. Open.

But, revealing a fragility few had anticipated, she fell short there and did so again in the finals of the two subsequent majors, most recently against Spaniard Garbine Muguruza in Paris on Saturday.

For Williams' coach, Patrick Mouratoglou, winning number 22 -- and thence upward to the all-time record of 24 held by Australian Margaret Court, who straddled the amateur and professional eras -- is still very much on the agenda.

"You can see blockages and mental problems. I see neither," he told reporters in the Roland Garros players' lounge after Saturday's defeat.

"I see how difficult it is to win a grand slam, how difficult to set all-time records... It will take the time it takes. It was tough to win the 17th, the 18th, it will be hard to win the 22nd and the 23rd but we will do it."


Williams could not have racked up numbers 19 to 21 any quicker, however, as she won the first three majors of 2015, putting her on course for the calendar grand slam that only Graf, Court and American Maureen Connolly have achieved.

But Williams unraveled in the U.S. Open semi-final against unseeded Italian Roberta Vinci, a player she had not conceded a set against in four previous meetings.

In January's final of the Australian Open, the American again failed to cross the finishing line, losing to German Angelique Kerber who won her first major having previously beaten Williams once in five meetings.

Chance number three to draw level with Graf came on Saturday in Paris, against fourth seed Muguruza, who Williams beat at Wimbledon in 2015 to win title number 21.

The previous day Williams appeared to view the Graf landmark with an uneasy mixture of fatalism and indifference, telling reporters "(there's) nothing I can do about it".

But in her final match in Paris -- perhaps in contrast to New York and Melbourne -- it did not appear to weigh her down.

She came up against someone who, in a high-octane final in which neither woman gave ground, played the better tennis and beat the American at her own power game.

Widely tipped after her win as the future queen of the sport, 22-year-old Muguruza will take some catching.

Does Williams, who turns 35 in September, have enough left in the tank to give chase?

Her coach believes she still has the game and, just as importantly, the passion to do just that.

"If she was indifferent about making history in her sport that would be a concern," Mouratoglou said.

"When there is tension and when the (opponent's) level of play is higher there are no more solutions. If (Serena's) game wasn't good enough to win this Roland Garros we have to do better next time."

(Additional reporting by Julien Pretot, editing by Toby Davis)