Stockley is understood to have caught the eye of Dons manager Derek McInnes during a fruitful loan spell with Exeter City this season.
The Grecians are also keen to sign permanently the 22-year-old and have reportedly already made the frontman two contract offers.
But the lure of top-flight football in Scotland and possibly playing in the Europa League could tip the balance in favour of Aberdeen.
Former Bristol City boss McInnes has drafted in a number of English players since taking charge at Pittodrie with Aberdeen guaranteed to finish as runners-up behind Celtic this season.
Poole-born Stockley impressed during his time at Exeter and netted 10 goals in 22 appearances for the Devonians, including scoring in their final two games of the season against League Two rivals Morecambe and Luton.
Grecians boss Paul Tisdale believes his club would be a good fit for Stockley. In an interview with the Express and Echo last week, he said: “Jayden has done particularly well and he is likely to have plenty of options available to him, but we would like to keep him.
“He has scored some important goals for us and added to our attacking options. We think he suits our style of play and our style of play suits him and, hopefully, he has enjoyed his time here and is keen to stay."