Aston has been Eagles boss since they were reformed in 1999
Sheffield head coach Mark Aston has turned down an approach for the same job at Harlequins, restating his desire to get Eagles into Super League.
The top-flight London club are looking for a new boss, following Brian McDermott's departure to Leeds.
Aston, also Eagles chief executive, told BBC Radio Sheffield: "I believe we can bring Super League to Sheffield.
"The future is rosy for the Eagles and with the backing of the public we can fetch Super League to the city."
He added: "If I believed we were always going to be a Championship team I would possibly have a look at what is right for Mark Aston and his family."