The Lilywhites are reportedly eyeing a January move for the 6ft 3in centre-forward, a player who crossed their radar last summer.
While there is interest in him, reports that North End are near triggering the buy-out clause in his contract are at this stage believed to be wide of the mark.
Stockley would fit the targetman role, one which has been vacant since Jordan Hugill's sale to West Ham United 11 months ago.
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Portsmouth and Sunderland have also been linked with an interest in the player.
The 25-year-old has scored 15 goals in League Two this season and found the net 25 times last term as the Grecians reached the League Two play-off final.
Poole-born Stockley started his career with Bournemouth and was loaned out eight times by the Cherries.
He moved to Aberdeen on a permanent deal in June 2016 and spent a season in Scotland before joining Exexter in August 2017 for an undisclosed fee.