The move comes after TVNZ officially launched a counter-attack on Henry this week, announcing Hilary Barry and Jack Tame will take over the Breakfast couch next month.
Details on the proposed move are limited, however, it's not expected to take place until the new year. It's understood Henry will not take over Garner's drivetime radio show.
Media commentator Bill Ralston said the move made "some sense".
"Why would they do it? I suppose because Paul's proved his success at Breakfast. He's taken ratings off TVNZ and threatened their Breakfast show to the point where they've had to make changes and bring in two very popular hosts," he said.
After successfully fending off competition from Paul Henry last year, this year has seen TVNZ's morning viewership decline significantly in the key commercial demographic of 25-54. At the same time, Paul Henry's viewership has seen strong growth.
While November saw Breakfast ratings peak with an average of 58,000 viewers (aged 25-54) per episode, this year has seen that number drop to an average of 39,000 viewers in June. Henry's ratings have continued to build, growing from an average of 11,000 viewers (aged 25-54) in April 2015 to 32,000 viewers in June.
Story has failed to build on Campbell Live's ratings performance, which saw the series placed under review in April 2015, before being axed.
Barry and Tame will begin hosting Breakfast next month, taking over from Rawdon Christie and Nadine Chalmers-Ross, who will both leave TVNZ.
In a statement, TVNZ head of news and current affairs John Gillespie said: "TVNZ had hoped to retain Nadine in another role but she has decided to explore other opportunities."
The new look Breakfast line-up, comprising Barry, Tame, weatherman Sam Wallace and newsreader Daniel Faitaua, will debut on September 16.
