AFL.com.au understands Cooney's manager, Marty Pask of Essentially Group, recently contacted the Bulldogs, saying Cooney wanted to finish his career a one-club player and was ready to talk about extending his contract, which expires at the end of this season.
But it is believed the Bulldogs told Pask they would prefer to defer talks until later in the season.
The Bulldogs preferred not to comment when contacted by AFL.com.au, while Pask did not return calls.
If Cooney, 27, remains uncontracted by the start of this year's free agency period on September 30 opposition clubs will be able to make official offers to him.
But, as a restricted free agent, the Bulldogs can keep Cooney simply by matching any offer.
Cooney entered this year on the back of two injury-plagued seasons when his degenerative right knee limited him to 27 games and made him a shadow of the player who won the 2008 Brownlow Medal.
But post-season treatment in Germany, which involved taking blood from his arm, separating and incubating its growth cells and injecting them into his knee, has helped Cooney train harder and perform better than he has in years.
After this season's first six rounds, he is averaging 23.5 possessions a game – his best return since 2010 – in a new role across half-back. He has also kicked nine goals.
It's form that will have sparked heightened interest from opposition clubs.
Former Bulldogs captain Luke Darcy told AFL.com.au last week Cooney's strong start to 2013 should ensure he re-signed with the Bulldogs beyond this season.
Cooney signed his current lucrative contract back in May 2010, at time when Gold Coast had approached him to be part of its inaugural list and when the right patella he cracked in the 2008 finals series had not yet degenerated to the extent of 2011-12.
Nick Bowen is a reporter with AFL.com.au. Follow him on Twitter: @AFL_Nick