"I think it's still in the pipeline, but my understanding is Devon's been spoken to and he's hopeful everything will be in place before that," he says. "I want him a part of that test squad, definitely."
Conway applied for residency last year but was told there is an eight-month wait due a Covid-enforced backlog.
It would mark a maiden test selection for the 29-year-old, whose value in the squad appears significant following a glowing valuation from Stead, who's put Conway in the class of veterans Kane Williamson and Ross Taylor.
"I knew he was a good player, I guess you can at times be pleasantly surprised around how people make that adjustment," Stead says.
"Devon looks like he's got all the skills of being an amazing player and I think we're really fortunate at the moment that we've had people in our squad like your Ross Taylors and your Kane Williamsons, and you see someone like a Devon Conway come along and think 'here's another guy who could also be in that class'."
Conway's enjoyed a blistering few months in the international realm, with his vast batting skillset mustering averages of 75 in ODI's and 59 in T20I's. Stead says that's helped create fierce competition within the squad which pushes up the performance standards.
"It provides an edge at trainings. The guys that have been brought into the team for the first time or returning players that have come back, to see all of them step up and put in a team performance... is most pleasing for me," he says.
The 20-man squad for the trip north will be named next week, and players who aren't competing in the Indian Premier League will return from leave and take part in camps in early May. Stead says they'll also look at a number of "standby players and make sure they're up to speed".
That squad will be trimmed to 15 for the Test Championship final.
Meanwhile, the coach has provided a promising injury update on skipper Kane Williamson who jetted off for the IPL on Thursday. Williamson was ruled out of the recent one-day series with Bangladesh due to a slight tear in his left elbow.
"He's started hitting balls again, he's had two or three hits and I know felt a lot better," Stead says.
"We expect he's going to be in much better shape than what he was before he had the rest and tidy-up around his elbow."