Subject to a number of conditions, the offer will be for the remaining AAPT shares that TCNZ Australia, which currently holds a 19.8 per cent stake in AAPT, does not already own.
Telecom NZ and AAPT have been in numerous discussions regarding ownership since May this year.
TCNZ Australia's offer follows a $1.49 billion hostile takeover bid for AAPT by Cable & Wireless Optus in April this year.
AAPT's board of directors voted unanimously to reject C&W Optus' offer on the basis it was "not reflective of the value of the company as it stands today", AAPT chief executive Larry Williams said at the time.
Paul Budde, telecommunications analyst said the merger between AAPT and Telecom NZ would be an ideal combination for the two companies.
"For Telecom NZ, the [New Zealand] market is far too small. They have exhausted what they can do there. From their point of view [the merger] is very understandable and acceptable," Budde told Computerworld Today.
"AAPT has grown to such a level, it needs large boots and with Telecom NZ it has that."
According to Budde, AAPT's decision to reject C&W Optus' bid did not have "anything to do with the money.
"It's the fit. AAPT and Telecom NZ fit - AAPT and Optus were competitors," he said.
"It would have been a disaster internally . . . In this situation, AAPT remains intact."
Meanwhile, Peter McIver, Deloitte's telecommunications partner is less confident about the deal.
"It's unlikely [AAPT] will accept," McIver said.
"Telecom New Zealand has waited its four months, I expect it would be rejected."
AAPT will not be available for comment until after the board meeting, officials said.
AAPT shares closed yesterday at $5.13 after trading as high as $5.18 during the past week amid takeover speculation.