It's understood Henry was TVNZ's first choice for Seven Sharp when the programme was originally created in 2012.
Instead, Ali Mau, Greg Boyed and Jesse Mulligan fronted the show, before Mike Hosking and Toni Street took over.
Henry claimed the Herald "was specifically told" that rumours he was heading to host a 7pm show on TV3 weren't true.
But the only contact the Herald has received from Mediaworks came on Friday afternoon, when a spokesperson said there would be "no comment" on the story. No further communications have been received from the broadcaster.
Henry repeated the denial in an interview with Fairfax, saying if it was to happen, he'd be the one to announce it.
"I am an exceptionally good communicator. If there was a change of this significance you can expect that I would be the one to communicate it," he said.
Last week, the Herald reported Henry will move to 7pm, with Garner taking over the morning slot, currently fronted by Henry, Ingrid Hipkiss, Jim Kayes and Verity Johnson.
It came after TVNZ confirmed it was replacing its Breakfast hosts Rawdon Christie and Nadine Chalmers-Ross with Jack Tame and former TV3 presenter Hilary Barry.