Correspondence delivered last week to Catalans warning them of legal action was sent by Hull KR's owner.
In an email obtained by the BBC, Neil Hudgell wrote to the Dragons to put them "on notice" if his club suffered "financial loss" due to the signing of Folau.
He said: "I reserve my position to take proceedings v Catalans Dragons."
Outlining the circumstances in which that might happen, the Hull KR chairman added: "For example, if title sponsor withdraws, or external investment is not secured, or quantifiable reputational damage is caused to the brand of Super League and its members."
Several other clubs subsequently told the Dragons they supported Hudgell's stance and would also consider legal action for damages.
It is also understood some believe they were not sufficiently consulted before the highly controversial signing was announced.
According to one senior club source, "nearly all" the Super League clubs have now endorsed Hudgell's threat.
It comes as the clubs prepare to hold crisis talks with Dragons chairman Bernard Guasch at a Super League board meeting in Salford on Wednesday.
Meanwhile, Dragons have cancelled a planned media appearance by Folau in Perpignan later this week as the row comes to a head.
He has begun training with Catalans, but the date of his Super League debut remains unclear as he undergoes numerous fitness tests.
Catalans Dragons, Super League and Hull KR have all declined to comment.
How did we get here?
Folau, who was sacked by Rugby Australia for homophobic social media posts in April 2019, has signed a one-year deal with the Dragons.
The 30-year-old was dismissed for saying "hell awaits" gay people, after previously being warned over his social media posts.
He sued Rugby Australia for $15 million, arguing he was a victim of religious discrimination, reaching a financial settlement in December.
Super League say "strict guidelines are in place" should Folau repeat such comments.
Folau said he "acknowledged the views expressed by Super League and the Rugby Football League".
"I'm a proud Christian, my beliefs are personal, my intention is not to hurt anyone and I will not be making further public comment about them," he said.
"I look forward to my return to the great game of rugby league with the Catalans Dragons."
The Rugby Football League and Super League said they "deplored" Folau's previous comments and it was "a difficult decision" to allow him into the competition.
In addition, the RFL said it did not have the "regulatory framework" to stop Folau from joining Catalans and as such could not "prevent his participation in the sport".
Catalans Dragons chairman Guasch said they "do not support or agree" with what Folau has previously expressed and "do not share or condone those views".
But he went on to say they "want to give Israel a new opportunity to shine on the pitch".
Halifax prop Keegan Hirst, Britain's first openly gay rugby league player, said the decision is "disappointing and frustrating".
Shortly after the Folau deal was released to the public, Wigan announced that their match against Catalans at the DW Stadium on 22 March would be "Pride Day".
The club said they are inviting LGBTQ+ groups to help promote equality in the game.
Folau's signing comes after the National Rugby League ruled out his return to Australia's top-flight competition.
He played in the NRL for Melbourne Storm and Brisbane Broncos and earned representative honours as a Queensland State of Origin player and Australia international