The City Reds have money to spend following the recent successful takeover by millionaire racehorse owner Dr Marwan Koukash and submitted a cash bid for the 26-year-old Chase.
The move was revealed by Castleford coach Ian Millward, who praised club chairman Jack Fulton for rejecting the approach for the 2011 Man of Steel.
"If he was looking at bailing out and getting in some money it would have been easy to say 'Dr Koukash come and get my man and give me a bundle of money' but he said 'go away we're not interested'," Millward told BBC Radio Leeds.
"That tells you what we're trying to do and how genuine and how good our chairman has been for us."
Salford had more success in tempting Griffin to join them on loan after he underwent a change of heart.
The 31-year-old former Wakefield, Huddersfield and England forward, a member of the Rhinos' Grand Final-winning team who is currently not figuring in coach Brian McDermott's plans, originally rejected their approach.
Salford coach Phil Veivers made his move for the experienced Griffin to bolster a squad depleted by a host of departures at the end of last season.
Veivers has signed Vic Mauro and Liam Foran from Manly Sea Eagles but they have yet to arrive in the country.
Griffin has joined Salford for a month and is set to make his debut against Hull KR at the City of Salford Stadium on Sunday after training with his new team-mates on Thursday.
- Sports & Recreation
- Ian Millward