The Australian superstar has been told he is surplus to requirements at Queensland Reds and the Dragons are looking to make him their second marquee signing after landing Lions back-row Ross Moriarty.
Head coach Bernard Jackman is also in the market for Wales star George North, who recently announced he would be returning back over the Severn Bridge on a National Dual Contract.
North will decide on his destination early in the new year, but it is understood the Dragons would only be able to recruit one of either Cooper or the Northampton wing.
Jackman wants up to 12 new players for next season and said: “It’s a chance to build something really exciting.
“Thankfully there are a lot of people interested in this sort of project. We are well on track for next season and our recruitment is going to be really impressive.”
Cooper has 70 caps for Australia and remains one of rugby’s biggest global stars.
Despite their interest in the former Toulon ace, the WRU-owned Dragons face stiff competition from a number of English, French and Japanese suitors for him.
The Dragons yesterday also confirmed the signing of Bristol back Jordan Williams for the start of next season on a two-year deal.