Fleming cited the example of Ricky Ponting doing a similar role with the Australian team last season.
Vettori was less inclined to pursue the national coaching gig away from his Royal Challengers Bangalore and Brisbane Heat commitments.
"I don't think I'd be available. I think it'd be a tough assignment for anyone [time-wise] but there's no doubt they have got a great group of players to build up towards a World Cup."
Shane Bond seems an obvious candidate, having been shoulder-tapped to coach New Zealand A to the subcontinent last year. However, it's unlikely he would forego his three-year commitment to the Sydney Thunder under their chief executive — and his former Canterbury teammate — Lee Germon.
Craig McMillan is expected to complete his batting coach tenure with the side at the end of the World Cup.
Much has been made of whether to split the head coach role, but examples of that working overseas have not produced definitive evidence to suggest it does. Besides, the commitments to the New Zealand team have hardly been taxing in recent winters.
In 2016, the Black Caps played two tests each against Zimbabwe and South Africa, last year they had the Champions Trophy and this winter there are no international games.
The decline in test matches and a lack of regular T20 internationals also suggest a split role might be excess to requirements.
If NZC follow a similar pathway to Hesson's selection, they will opt for a character who prefers to work in the background on systems and analysis rather than a frontman whose name comes emblazoned in neon lights.
Calls placed around the cricketing traps gravitated back to Canterbury coach Gary Stead and Central Districts coach Heinrich Malan as key contenders.
The 46-year-old Stead has guided Canterbury to three Plunket Shield titles in the past five seasons and the 2016-17 Ford Trophy.
Malan helped CD to last season's Plunket Shield and back-to-back Ford Trophies in 2015 and 2016.
The 37-year-old told the Hawke's Bay Today he was undecided about applying.
"If a process is put in place, and the change presents itself, I will take a look at it then but until we know how that'll pan out it's a pretty tough position to say if you will or you won't."