The state broadcaster's head, Rick Ellis, Friday night suggested Henry's future was far from certain, despite his earlier stand that Henry's job was not on the line, the New Zealand Herald reported.
"I think that as the week has progressed and the complaints have continued to roll into the company, you've really got to reassess things each day and I'll be reflecting over the weekend and again on Monday as to where we go from here."
The bleak signal for Henry came after Maori Affairs Minister Pita Sharples said in an interview with current affairs show "Marae Investigates" that Henry should go.
The interview screens Sunday at 10 a.m. on TVOne.
Sharples is the second senior minister to cast doubt over Henry's position as "Breakfast" co-host.
Earlier, Communications Minister Steven Joyce suggested Henry was becoming a liability.
The criticism comes against a backdrop of intensifying diplomatic fallout in India where Henry's outburst has drawn strong reaction from the country's government.
Asked if he thought Henry was racist, Ellis said: "I'm not sure I'm going to answer that question because I don't want to be drawn into this whole debate about whether Paul Henry is racist or not."
"Certainly the comments that he's made have clearly been of a racist nature and they could only be interpreted that way ... as a person deep down I think he's a very decent human being."
The fallout from Henry's questioning of whether the Indian-origin Governor-General, Sir Anand Satyanand, was "even a New Zealander" and whether the next governor-general would "look and sound like a New Zealander" has included hundreds of complaints to the broadcaster.
The issue has been compounded by Henry's earlier mockery of an Indian chief minister's name.
Henry, who was suspended Tuesday, deliberately mispronounced Delhi Chief Minister Sheila Dikshit's name, despite being told it is said "Dixit". He also said the name "Dick Shit" is "so appropriate" because she is Indian.
Senior TVNZ management have faced criticism about whether lax management of Henry led to the situation.
Ellis said he had taken steps to tighten editorial guidelines. "From time to time you do need to revisit the discipline around the implementation of editorial policies and that's what we're going to do."
Prime Minister John Key Friday continued to dismiss Henry's mockery of Dikshit's name as a joke which got out of hand.
New Zealand's High Commissioner in New Delhi, Rupert Holborow, has apologised for Henry's "racist, insensitive, inappropriate and vulgar" mocking of Sheila Dikshit's name after India summoned him to make a formal protest.
India's High Commissioner in New Zealand, Admiral (Retd.) Sureesh Mehta has also written to broadcasting minister Jonathan Coleman to protest about it.
Foreign Minister Murray McCully Friday described Henry's comments as "gratuitous and insulting" when responding to the diplomatic action taken by India.
Coleman also said he was not surprised people found the comments "offensive and inappropriate".
Key said he did not intend to make contact with the Indian government, saying the high commissioner's apology was in effect an apology from himself.
Labour leader Phil Goff said Key could not afford to try to deflect the situation by downplaying it.
"He has to say this is totally unacceptable and offensive. We are right in the middle of trade negotiations with India."
Media in India have widely covered the issue, including reporting that Indian ministers boycotted a dinner with Sir Anand, who is in India.
YouTube clips of Henry's comments have been replayed by Indian television stations.