Collingwood president Eddie McGuire and former Western Bulldogs club champion Luke Darcy have suggested there will be outrage from other clubs if free agent Franklin, a dual Hawthorn premiership player, joins the Swans.
Greater Western Sydney on Tuesday pulled out of the race to sign Franklin and fired a parting shot at Sydney for making a significantly higher offer.
GWS say they've been advised by Franklin's agent Liam Pickering that the superstar forward is headed to the Swans.
"We put forward what we believed to be both a sensible and attractive offer to Franklin," GWS chief executive David Matthews said in a statement.
"Contrary to media reports, that offer was $1.2 million a year over six years.
"It appears he has a significantly higher financial offer which we would not have been prepared to make based on our due diligence."
Sydney added to their 2012 premiership side by recruiting ex-Adelaide key forward Kurt Tippett. Brereton says the likely signing of Franklin will place massive strain on Sydney's ability to remain competitive.
The Swans achieved a top-four finish in 2013 but Brereton says long-term success could be in doubt.
Hawthorn great Brereton, who also played seven games for Sydney, says Melbourne clubs will be furious if Franklin heads to the Swans.
"The same will happen again (as the Tippett reaction)," said Brereton, who mentors the forwards at GWS.
"I say good on them if that's the way they (Swans) want to go.
"The one thing the rest of the clubs will do (is argue their case).
"The other clubs who don't receive a cost-of-living allowance ... it's a fair whack.
"It's pretty apparent now that cost-of-living excess that they (Swans) get is just going straight into the procurement of champion players.
"You can say the cost of living in Sydney is high and perhaps it is. But you don't actually have to live in the centre of town.
"You'd have to say that it's actually going somewhere else rather than the rank-and-file player who's at the club.
"You've got two players - Tippett and Franklin. If they both play in the same team next year, 36 other players aren't getting a share of that cost-of-living allowance."
Darcy told Melbourne's Triple M radio: "I think there would be a riot. There would actually be a riot in AFL football."
McGuire, a long-time critic of the Sydney clubs' allowances, agreed, saying: "I think so."
A spokesman for the Swans was unavailable for comment.