Addo-Carr and his manager met with Bulldogs football boss Phil Gould on Monday evening, after details of his roadside test emerged.
Gould said the Canterbury flyer had told him he did not know why he had tested positive, and vehemently denied taking any drugs to lead to the result.
Gould will meet with Canterbury coach Cameron Ciraldo and club bosses on Tuesday, before they decide whether to name Addo-Carr to face Manly on Sunday.
"Josh has had a lot going on in his life in recent time. Injury, family, people close to him with their families," Gould said on 100% Footy.
"I think it's been a tough time for him off the field, and we have to be mindful of the fact we have a big game and we can't be distracted.
"Josh has indicated he wants to play, and I have spoken to the NRL integrity unit and as of this point, they would have no reason to stop him from playing.
"But that is a discussion for the coach and chairman when I sit down with them tomorrow, and Josh, when we get a little bit more information."
Addo-Carr's alleged positive test threatens to overshadow Canterbury's first finals match in eight years.
The winger was advised not to attend the club's presentation night on Monday, as the drama played out.
Police pulled the Bulldogs star over around 10.45pm on Friday night while he was driving in Wentworth Point, a suburb in Sydney's inner west.
Addo-Carr is alleged to have tested positive to cocaine but the 29-year-old has not been charged, pending further analysis of his sample.
"About 10.45pm on Friday (6 September 2024), officers attached to Auburn Police Area Command were patrolling Baywater Drive, Wentworth Point, when they stopped a Toyota hatchback for random testing," a NSW Police statement read.
"The driver - a 29-year-old man - was subject to roadside testing which allegedly returned a positive indication for cocaine.
"The sample has been sent for analysis."
Gould said Addo-Carr had approached the club on Saturday morning to inform them of the matter, but said the winger had told him the test was inconclusive and there was no issue.
It was only when the club received phone calls about the matter on Monday they discovered that the Kangaroos Test star had allegedly returned a positive sample.
"He came in and reported it to us the next morning, but the way it was reported to us, he was very dismissive of it," Gould said.
"That there was no drama, he hadn't tested positive to anything, they had allowed him to drive home.
"What Josh thought was because he went and did the second test and they allowed him to go, he thought it was negative.
"I'm not saying Josh was deliberately misrepresenting, that was his interpretation of events. The police have a different interpretation."
Addo-Carr had been ruled out of Canterbury's loss to North Queensland last weeekend due to an ankle injury, and had spent Friday night at the South Sydney-Sydney Roosters match.
An NRL spokesman confirmed to AAP the league was aware of the matter and was "liaising with the club".
Addo-Carr's alleged positive test came amid Operation RAID, a state-wide operation targeting traffic offences between Thursday and Sunday morning.
In total, the operation detected 470 alleged drug drivers from 10,885 tests.
