Jeggo, who excelled in his debut season for the Reds, was born in the Austrian capital of Vienna and has been identified by Sturm's German coach Franco Foda as a player of interest.
It’s understood the club, which finished fourth in Austria's Bundesliga last season, wanted to take a closer look at the A-League's Young Player of the Year during a mooted two-day visit this month, with a view to offering him a contract.
The three-times Austrian champion, which has also won seven domestic cups down the years, tabled a letter of invitation for Jeggo to travel but failed to sway Adelaide chiefs, who are reluctant to entertain the prospect of losing a key player who still has a year remaining on the deal he signed on arriving from Melbourne Victory last season.
Jeggo's agent, Sydney-based Buddy Farah, said: "James is a contracted player and Adelaide holds his contractual rights and at this stage I have no further comment."
Sources in Austria indicate Sturm is looking to snare Jeggo, who left Austria as a 10-year-old when his father landed a job at the CSIRO in Melbourne, on a free transfer after being impressed by his form for the Reds over 31 games in all competitions last season.
That included winning the FFA Cup and coming within a game of reaching the A-League decider, before the Reds were unceremoniously eliminated by Sydney FC 4-1 in the semi-final.
The sole Australian playing in Austria's top flight is Socceroos midfielder James Holland, who is looking to move on after four successful seasons with Austria Wien - which finished seventh on the ladder, 15 points adrift of Sturm Graz.