Kenrick declined to comment on this suggestion out of respect for the family's request for privacy.
Asked if the state broadcaster would be doing more to support its staff, Kenrick said it absolutely would be.
"I think this is something that has profoundly affected us as an organisation."
He said the situation would bring the people at TVNZ together more tightly as a group and more would be done to support people and "recognise this is a people-driven industry."
TVNZ staff had conducted a karakia to remember Boyed in the newsroom.
People from around New Zealand have expressed their shock and sadness at Boyed's sudden death.
TVNZ's Head of News and Current Affairs, John Gillespie, said the news has come to a huge shock to all at TVNZ.
"Greg was a prominent figure in our newsroom for the last 25 years. He was a wonderful man and a talented broadcaster who strongly believed in the power and importance of journalism in people's lives. Greg was known for his warmth and kindness. It's a very personal loss for us.
"Greg will be missed by us, he will be missed by our colleagues in the wider industry and he'll be missed by our viewers. Our thoughts are with Greg's whānau and friends."
His family released a statement saying he will be deeply missed.
"He was absolutely loved and adored. A treasured son, brother, husband and father, he will be deeply missed.
WHERE TO GET HELP:
If you are worried about your or someone else's mental health, the best place to get help is your GP or local mental health provider. However, if you or someone else is in danger or endangering others, call police immediately on 111.
OR IF YOU NEED TO TALK TO SOMEONE ELSE:
• LIFELINE: 0800 543 354 (available 24/7)
• SUICIDE CRISIS HELPLINE: 0508 828 865 (0508 TAUTOKO) (available 24/7)
• YOUTHLINE: 0800 376 633
• NEED TO TALK? Free call or text 1737 (available 24/7)
• KIDSLINE: 0800 543 754 (available 24/7)
• WHATSUP: 0800 942 8787 (1pm to 11pm)
• DEPRESSION HELPLINE: 0800 111 757
