Their fate will lie in the hands of teammates, with the Kiwis senior leadership group, coach David Kidwell, campaign manager Shane Richardson, and Hayton, due to assemble for a meeting later this week to determine what action will be taken.
"That could be one of the possible sanctions but until we get the group together and we work through that it will just be speculating but it is one of a number of options," said Hayton.
"The players have breached their code of conduct as governed by the collective bargaining agreement which includes representative matches involving New Zealand, so the clubs will look into that.
"But separately it was on international duty so we need to look at it and impose what we think are appropriate sanctions because of how it affects the Kiwis and New Zealand Rugby League."
Both Bromwich and Proctor expressed their extreme sorrow and regret through prepared statements released by their respective clubs.
Both admit to drinking too much throughout the night and while Bromwich did not refer to the incident in his statement, Proctor did not deny what is alleged to have occurred.
"After the game we went back to the New Zealand team hotel and had a late dinner," Proctor's statement read.
"After dinner we went to a local club to have a few drinks. The rest of the night is a bit of a blur as I obviously had too much to drink before the incident that has caused all of the trouble which happened much later in the night.
"Although I can't remember exactly what happened I don't deny it."
Titans chief executive Graham Annesley intends raising with the NRL the issue of supervision of players whilst away from their clubs on representative duties.
Hayton confirmed the pair was among a group of players and team staff that went out for "a quiet drink" following dinner, but was unsure if they had stayed out alone or returned to the hotel with the others before going out a second time.
"I will need to have a discussion with team management just to understand what was in place and so I can't really comment any further," he said.
Auckland-born Bromwich will donate his Anzac test match fee to a selected charity and has been ordered to undergo counselling and treatment courses.
The Titans are providing Te Kuiti-born Proctor with welfare and support to ensure his general well-being.
