The National Party leader told reporters at Auckland Airport that more progress was made in talks this afternoon with the Act and New Zealand First leaders.
He said there were more conversations to have about who would be deputy prime minister.
"We'll have more to say about that shortly but we really are very close and we are just in the final stages. There's more conversations to have but we can do that from Wellington tonight."
Act leader David Seymour also flew to the capital this evening and NZ First's Winston Peters is expected to fly down tomorrow.
Some senior National MPs, including deputy leader Nicola Willis and Chris Bishop have already returned to Wellington, with Willis telling RNZ she was not in line for the position of deputy prime minister, which is understood to be between ACT leader David Seymour and NZ First leader Winston Peters.
It has now been nearly six weeks since the 14 October election, and almost three weeks since the final vote total was announced.
Special votes saw National and Act lose their majority, meaning they need NZ First to form a government.
Earlier today Luxon said that the third and final stage of the negotiations is "largely" finalised, but it's "fair to say" the deputy prime ministership is a sticking point.
"Suffice to say we've got a couple of issues to close out and then we can get this thing done ... largely we've agreed our ministerial positions and appointments," he said.
ACT leader David Seymour and his deputy Brooke Van Velden arrive in Wellington on Wednesday. Photo: RNZ / Ashleigh McCaull
ACT's Seymour flew to Wellington on Wednesday evening with his deputy Brooke van Velden, but he said nothing should be read into the trip.
"It looks like a deal is close enough that we're getting a flight that we can to get down to Wellington. Classic, only in New Zealand, we've got to go down because there's been some fog and it's hard to get a flight."
