Graham is contracted with the Tigers for next year and he told reporters he was only in Adelaide to visit family.
But it seems that family visit has now involved a trip to Alberton, where Graham met with Hinkley and other members of Port Adelaide's hierarchy on Wednesday.
With GWS pair Jacob Hopper and Tim Taranto keen to join Richmond, Graham is heavily considering a move away from the Tigers.
On Tuesday, Port Adelaide's football manager Chris Davis confirmed Graham was among a number of South Australian-born players that were on the club's radar.
Graham finished second in Richmond's best and fairest count last year and the 24-year-old also featured in the club's flag-winning campaigns of 2017 and 2020.
Port Adelaide are in the box seat to secure premiership forward Junior Rioli, who has already told West Coast he wants to be traded to the Power.
Meanwhile, Brisbane have put to bed any speculation they would be willing to trade 2017 No.1 draft pick Cam Rayner.Â
Rayner averaged 14.7 disposals an d booted 24 goals in a breakout campaign this season and the Lions confirmed he is not up for trade.
Brisbane announced on Wednesday they have re-signed Jaxon Prior, Carter Michael and Blake Coleman.
Prior has put pen to paper on a two-year contract extension to remain a Lion until at least the end of 2024, while Michael and Coleman have signed one-year deals for 2023.
Fremantle have met with Gold Coast forward Josh Corbett.
Corbett is out of contract and the 26-year-old is weighing up his future.
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