Peter Nevill could find himself promoted to number six in Australia's batting order for the first Test against West Indies next month, coach Darren Lehmann has said.

Wicketkeeper-batsman Nevill played a key role in helping Steve Smith's side to a three-wicket victory over New Zealand in the inaugural day-night Test in Adelaide, striking 66 in Australia's first innings as the hosts recovered from 116-8 to post 224.

That valuable knock represented the highest score of the match and Nevill's best in seven Test outings since he replaced Brad Haddin behind the stumps.

Lehmann has previously hinted at sending Nevill in ahead of all-rounder Mitchell Marsh and again acknowledged the switch could take place when Australia face the Windies in Hobart from December 10.

"The captain has talked about that, maybe for the next Test against the West Indies, depending on the make up of the side," Lehmann told ABC Grandstand.

"End of the day, we'll sit down as a selection group tomorrow [Monday], get that sorted."

Although Nevill averages just 27.30 in Tests thus far, Lehmann is confident the 30-year-old has what it takes to thrive higher up the order.

"Peter Nevill's record in first-class cricket [in which he averages 41] is fantastic," added the head coach.

"He's a great technician. He doesn't have the power of Haddin or [Adam] Gilchrist, but what he does is play the situation really well.

"I was really pleased with Nev's performance in this game under pressure with the tail, and that's what you expect from a keeper who's taking over from a couple of the greats of the game."