Klein gives the following etymology for navi:
Probably derived from the base נבא (= to call, proclaim); accordingly the original meaning of navi probably was 'the man who calls or proclaims'.
He then has this entry for the root נבא:
Akkadian nabu (=to call, announce, proclaim), Arabic naba'a (= he uttered with a low voice, announced), naba' (= announcement, information), nab'ah (=a low sound).
This article by Daniel E. Fleming quotes Albright as saying that navi
is a noun from a passive form of the Semitic root nb', "to call"... The prophet is therefore "one called" by God.
In the end, he prefers this theory:
The Syrian nabu is best understood as one who invokes the gods, and the noun should be an active participle from the verb nabu, "to name." ... the Hebrew nabi is best explained by the same etymology.
The Ben Yehuda dictionary says that the Arabic verb meaning "to announce, inform," had the sense of someone walking from land to land, and perhaps this sense of walking from place to place was the original meaning, since these kinds of travelers would be the ones to inform.
The same source also suggest another theory, which connects it to a different Arabic root meaning to "wake from sleep", in which someone's heart is suddenly awake with the need to speak about something.
Returning to the Akkadian connection, the Akkadian dictionary has the following entry for nabu:
G. to name (+2 acc.) ; to invoke (a god) ; to nominate ; to decree, ordain D. to lament, wail Š. to cause to proclaim N. to be named ; to be appointed, called upon
This last sense, "to be appointed", calls to mind a suggested etymology by my friend Michael Gerver. He wrote:
Although I have not seen this suggested anywhere, it seems possible that Arabic nawaba, “represent,” “substitute,” is related to Hebrew נוב, “speak,” if the Arabic word originally meant “speak for.” Arabic nawaba is the source of Arabic na’ib, “viceroy,” whose plural nuwab is the source, via Hindi or Urdu, of English nabob
Even if nawaba doesn't mean "to speak for", it could still be connected to nabob via the Akkadian "appoint". Here is the Online Etymology Dictionary entry for nabob:
1610s, "deputy governor in Mogul Empire," Anglo-Indian, from Hindi nabab, from Arabic nuwwab, honorific plural of na'ib "viceroy, deputy," from base n-w-b "to take someone's place." Also used of Europeans who came home from India having made a fortune there, hence "very rich man" (1764).
I also have no proof of this (although as always, I welcome help from readers), but I relish the opportunity to discuss nabob (which can mean "important person" in addition to "rich man"), as it was used so masterfully by my inspiration for this blog, William Safire. When Safire was a White House speechwriter in 1970, he wrote a speech for Vice President Spiro Agnew that used the phrase "nattering nabobs of negativism." It is one of the most famous quotes associated with both Agnew and Safire.
I've always loved the phrase - but until now, had no idea that nabob could be perhaps related to navi...