The show, broadcast at 7pm on weekdays, was launched in 2017 and is hosted by Jesse Mulligan, Kanoa Lloyd and Jeremy Corbett, who are usually joined by a guest fourth host.
About 24 staff work on the programme.
A Warner Bros. Discovery spokesperson said: "We have commenced consultation to discontinue The Project on Three from the end of the year - our primary focus is to support our people as we work through this process."
Senior director of news Sarah Bristow announced the proposal to the Newshub team on Thursday.
"If the proposed change is confirmed, we will design a redefined news show in the 7pm timeslot as part of the broader Newshub proposition," said Bristow in the email.
"I want to acknowledge the hard work of Jesse, Kanoa, Jeremy, Jon Bridges, Ali Ventura and the entire crew of The Project, who have worked tirelessly to bring this show to air for the past seven years.
"The Project has served Newshub and Three incredibly well since its commission back in 2017, however audience behaviour has changed dramatically since that time."
Bristow said in a statement on Newshub's website that this year the company had been transitioning the broadcast business to a digitally led operating model and the transformation of the newsroom was equally crucial.
It needed to be "more responsive to audience needs across the day".
"We have been reviewing all areas of our business to reimagine what our on-air news offering would look like, if we were to build it again from the ground up - the focus being to capture digital audiences and drive online engagement as we have successfully done with Paddy Gower Has Issues.
"There are no proposed format changes to other Newshub shows."
Warner Bros Discovery ANZ senior vice president and head of networks Glen Kyne said the decision had not been made lightly.
"This is a strategic proposal for our business as we move to a digitally led operating model and look to redefine our 7PM proposition in line with our commissioning strategy," he said in a statement.
He praised those who had worked on the show.
