Can you elaborate a bit on what you mean, particularly terminologically?

"Persia" usually refers to the historical region controlled by empires centered in what would now be Iran (as that country has been known since the early 20th century.) Maximally defined this "greater" historical Persia covers a pretty huge territory. The use of "Persia" or "Iran" to describe these territories is imprecise, and well-meaning historians differ on usage, so, for instance, you have The Cambridge History of Iran but a work like David Morgan's Medieval Persia: 1040-1797.

"Farsi" is the contemporary Persian language (i.e. the language of ethnic Persians), and as a result is often called "Persian Farsi", although there are other dialects of Persian, like Dari in Afghanistan.

Azeri or Azerbaijani is a Turkic language/dialect spoken by Azerbaijani Turks with a very high level of mutual intelligibility with Turkish (as spoken in the Republic of Turkey.)

The modern Republic of Azerbaijan was a part of Persian territory until it was taken over by the Russians in the early 19th century and subsequently gained independence in the 20th.

While Azerbaijan is an independent nation state, the large portion of ethnic and linguistic Azerbaijanis that still live in north-west Iran actually make Iran home to most of the world's Azeris, and as a result today they make up Iran's second-largest ethnic group. They are nonetheless dwarfed by the majority Persian population, and the Azeri language does not have official status in Iran, where Farsi is the sole official language.

The territory of historical Persia has been ruled, in the past thousand some-odd years, by a variety of ethno-linguistic groups including Arabs, Persians, Turkic peoples, Mongols, and so on.

That being said, I can't see any plausible way in which you could say that Persia is Azeri in either historic or modern terms. Portions of modern Iran are majority Azeri and they form a large portion of Iran's modern population. But Turkic peoples, including the Azeris are not, and to my knowledge never have been a majority of the total population of Persia, although "Greater Persia" perhaps complicates that reckoning.

In any event, the use of Persian/Farsi as the binding lingua franca of this region is the raison detre for "Greater Persia" in the first place. As such I think if I had to choose I would emphasize the Persian language (i.e. Farsi) identity of the region, while noting the long history of a Turkic presence, of which the Azeris are part.

In other words, this is a ethno-linguistically complex region, and I would hesitate to say that it is one thing or another, but hegemony of the region by Persian speakers for several thousand years is arguably its defining feature.