A photo posted by Paulo on his Instagram account allegedly showed the trio dining with former senior Nomad boss Paulie Younan and accused fraudster and money launderer Rafat Alameddine last Friday night, according to Fairfax Media.
Parramatta duo Norman and Paulo, along with fellow NRL player Segeyaro, were issued with official warnings by NSW Police.
"Organised Crime Squad detectives have issued consorting warnings to three current NRL players under section 93x of the Crimes Act 1900," NSW Police said in a statement.
"The warnings were issued to three men aged 22, 25 and 26."
Under the terms of the act, a person can be charged with consorting if they habitually consort with convicted offenders.
To be classified as 'habitually consorting', a person must consort with at least two convicted criminals, and consort with each convicted offender on at least two occasions.
NRL chief executive Todd Greenberg said all NRL players and officials must choose their friends and associates wisely and take the police warnings seriously.
"This reflects poorly on the players involved and is a bad look for the game," Greenberg said in a statement.
"I would expect those who have received warnings to take them very seriously.
"The penalties for ignoring a warning are severe and we fully support the police in the action they have taken."
The maximum penalty for consorting is three years in prison.
Fairfax media said the photo was believed to have been taken hours before a group of men, including Norman, were stopped from entering The Star casino when security officers found a container of pills, which where were later sent for analysis.