The Daily Telegraph's Phil Rothfield identified the player in question as Bulldogs prop Aiden Tolman, whose child attends Laguna Street Public School in Caringbah in Sydney's south, where a teacher tested positive for COVID-19 on Friday.
The Roosters-Bulldogs game, scheduled for 6.05pm NZT today at Bankwest Stadium in Parramatta, has been pushed back and will now go ahead at 9pm NZT tomorrow night if Tolman returns a negative test.
In addition to Tolman, Weidler has reported the entire Bulldogs team may also need to undergo tests.
St George and Cronulla, who were slated to face off at 6.30pm tonight at Campbelltown Stadium, will now play at 4.05pm and the game will be broadcast on Channel 9.
Bulldogs CEO Andrew Hill said Tolman was "in a bit of a panic" when he called the club on Saturday night.
"Aiden Tolman called me in a bit of a panic at about 8pm and said that he'd just received advice from the school that one of the teachers had tested positive," Hill told Nine's Sunday Footy Show.
"We immediately worked with the league and at that stage we weren't sure of what the outcome was. We thought perhaps it was just that Aiden may have missed the game but clearly overnight and early this morning we'd been advised the risk is too great and we've all agreed to postpone the game."
Hill added: "At the beginning of this process, everyone in the game gave a really strong commitment to consider the community and follow a safety-first attitude. Obviously, that's what we're all doing.
"I think the risk will be really low but let's just get through the next few hours and worry about the next step then."
Australian Rugby League Commission (ARLC) chairman Peter V'landys said players' safety was the league's top priority.
"We're not prepared to risk it," he told The Telegraph. "The health of the players come first."
In a statement, V'landys added: "There's a very remote risk of infection within the Bulldogs squad. To ensure there is no risk at all, the player will be tested today and the game delayed until tomorrow to ensure the test results have returned.
"I want to congratulate the Bulldogs for swiftly informing the NRL.
"I want to thank our broadcast partners for their assistance, at very short notice, in changing the schedule. The changes will ensure our fans will still be able to watch a game on free to air television this afternoon."
All students at Laguna Street Public School have been instructed to self-isolate after a staff member tested positive to COVID-19. The school will also stop on-site learning until June 24 following the diagnosis, according to the NSW education department.
"The staff member has had contact with most students at the school during the period they may have been infectious," a statement from the department said on Saturday night.
Apart from minor incidents such as Wests Tigers star Benji Marshall kissing a reporter and Bulldogs legend Terry Lamb shaking hands with players at training, this is the first major setback the NRL has encountered since it successfully relaunched its season late last month after a lengthy hiatus because of the global pandemic.
Its planned restart date of May 28 was deemed too ambitious by some but V'landys ploughed on, determined to make it work and the first two weekends went off without a hitch.
It was a huge victory for rugby league as it enjoyed clear air in Australia, returning two weeks before the AFL got back underway on Thursday night.
After losing their first two games before the season was suspended because of coronavirus, the Roosters have bounced back with convincing wins over Souths and the Broncos.
The Bulldogs lost their first three matches but trounced the Dragons 22-2 last week to ease some of the pressure on coach Dean Pay.
