It is understood that club officials are exploring the possibility of adding the 30-year old if he came on a reduced salary.
It has been reported that Hayne is chasing a figure in the $700,000-$800,000 ball park, a price Canterbury would not be willing to pay.
Bulldogs board members are not looking to interfere with the club’s recruitment plans, but are merely assessing whether or not Hayne is financially attainable.
Hayne’s preference is to remain in Sydney but has attracted interest from the French rugby union as well as the St George Illawarra Dragons.
It is still possible that the former San Francisco 49er remains at Parramatta should the Eels free up salary cap space by shipping Michael Jennings to the Knights, who is coming off contract and looking for a longer deal.
Hayne told The Daily Telegraph last week: “I’m going to have to (look for another club) because I don’t have a job. In four days, my contract is over. It’s a bit of a lottery (where I will be in 2019).
“I’m on the market, looking for a job. I’ve got to pay the bills.”