Mr Maxwell's popularity with the board is despite a petition last August from two-thirds of Maori TV staff expressing concern about his possible appointment.
Reports of his status as a frontrunner have revived questions about processes at Maori TV which has an annual budget of $45 million of taxpayers' money.
Mr Maxwell is seen as being more conservative than his predecessor, Mr Mather, who has been allied to the popular head of news and current affairs Julian Wilcox and head of production Carol Hirschfeld. Both were early applicants knocked out of the running by the board.
Maori educationalist Richard Jefferies remains a contender.
A row blew up last September over the resignation of Maori TV board member Ian Taylor over the chief executive appointment process. Mr Taylor's resignation led to the process being put on hold.
It is understood one member of the board has consistently opposed Mr Maxwell's application but that the board has changed rules so that the appointment does not have to be unanimous.
Maori TV is overseen by Finance Minister Bill English and Maori Affairs Minister Pita Sharples and Labour is expected to ask questions about the appointment process in Parliament today.
Alan Witherington is leading Maori TV as interim chief executive.
Mr Maxwell, Mr Dagan and Mr Kenrick did not return calls.