No, she hasn't exactly declared herself a candidate for the post, which will be decided at the party's conference in November but, in her usual candid style which leaves the door wide open to interpretation, hasn't denied her interest in the job either.
"Why not?" she replied when asked the question recently in a radio interview.
"Collectively there are several of us. So why not?"
Hmmn most revealing, isn't it?
Was she talking about several women joining forces to lead the party forwards?
Or perhaps she was borrowing something from the more diplomatic proposals from a former prime minister and current Mayor of Bordeaux Alain Juppé that there should be some sort of joint presidency to prevent infighting splitting the party.
Anyway, with Dati's arch enemy and former prime minister François Fillon having already announced he's standing and the party's current secretary general Jean-François Copé clearly in campaigning mode, November looks as though it could be a real handbags at dawn affair.
As for Dati's precise intentions? Well remember this is (French - although it's probably not so different elsewhere) politics where allegiances are built on the proverbial shifting sands and personal ambition often rides roughshod over ideology or the common good.
So Dati, although equally as firm in her support for Copé as she is for her dislike of Fillon, probably wouldn't mind positioning herself for a run at the Really Big One if the opportunity presented itself, is keeping her options open.
The most prominent element missing from any party battle in November will most likely be exactly what Dati and many other female politicians bemoan - the presence of a woman in the race.
Ah yes. Women in French politics - they get a pretty rough deal.
How many can you name for example (without resorting to Google)?
From the Socialist party, which currently holds all the country's major offices, how many come to mind immediately apart perhaps from the usual high profile suspects such as Ségolène Royal and Martine Aubry.
After that it gets kind of tough doesn't it?
And what about that apparent balance between men and women in the government, so highly touted by the French president François Hollande and his (male - just in case you needed reminding) prime minister Jean-Marc Ayrault?
|Family photo - Jean-Marc Ayrault's first government (screenshot BFM TV)|
Oh yes there's the same number of men (19) and women (19) and many have held that up as an example of Hollande succeeding where his predecessor, Nicolas Sarkozy, so obviously failed.
But, as has also been pointed out several times, the jobs haven't exactly been shared out equally when it comes to the pecking order.
Take a look at the so-called "top jobs" (for want of a better expression) for example; the foreign minister - Laurent Fabius, the interior minister - Manuel Valls, the defence minister - Jean-Yves Le Drian and goodness, the justice minister - Christiane Taubira. A woman!
One out of four. Not bad.
Certainly ain't real parity though, is it?
Clearly there weren't enough qualified women to go around for those positions.
Marisol Touraine (social affairs and health), Aurélie Filippetti (culture and communication) or Delphine Batho (ecology, sustainable development and energy) certainly aren't going to kick up a stink about the portfolios they've been given at some equally important but arguably less prestigious ministries.
But Ayrault (and Hollande) surely limited their choice by plumping for women who were parliamentarians - from the National Assembly or the Senate.
And therein lies part of the problem for any real gender parity in government - at least in France.
The last election returned the highest number of women to the National Assembly the country has ever seen.
That's the good news folks.
But when you look at the actual figures, you discover a different story.
Of the 577 députés, a whopping 155 were women.
All right that was up from the 109 of the 2007 elections but it still only accounts for 27 per cent of those elected to the National Assembly.
Progress - very slow progress - which will see France rise from 70th in a table of women members as a percentage of the total number present in the country's lower house to 36th - nestled just between Afghanistan in 35th and Tunisia in 37th.
Still at least that's better than the UK down in joint 55th with Malawi.
Maybe there's something after all to the much-quoted comment by the late journalist and politician Françoise Giroud that there'll only be real gender parity in politics when "a woman is appointed to office on the basis that she is just as incompetent as a man."
Les nouveaux ministres posent pour la photo de... par BFMTV