The Sharks have offered Ramien a $2 million four-year deal, but must first shed players to create the necessary salary cap space.
The club will reportedly ramp up its bid for Ramien once it officially bows out of the finals race.
Matt Prior has been linked to Parramatta, while Dugan is a player the club have identified that they would be willing to part with.
Ramien was released from the Knights after June 30 under Nathan Brown’s watch, however, the club has shown interest in re-signing him on bigger money.
The 22-year old’s preference was always to return to his former club Cronulla.
Newcastle-bound Jayden Brailey said Ramien would be welcomed back to the Sharks with open arms.
“He played his best football here, he was happy here at Cronulla, and if he came back he’d click into gear and have a good season,” Brailey said. “I’d love him to come back up to the Knights. It didn’t work out for him personally, and I wish him all the best wherever he is.”