Hayne is contracted to the Titans for 2018, but has a clause in his favour allowing him to walk out at the end of this season if he chooses.
Hayne must decide before the end of May if he wants to activate the final year of his $1.2 million-per-season contract with the Titans.
The Eels will be unwilling to match Hayne's deal at the Titans for next year, according to the report, and will be around AU$400,000 short of Hayne's current deal.
On Sunday, Fox Sports' Paul Kent told Triple M, Hayne has continued to have a negative impact on the Gold Coast with his lazy training methods resulting in coach Neil Henry putting every player through additional drills at the end of training.