Juve scouts have been impressed by the youngster, who moved to Salzburg from Bayer Leverkusen.
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La Gazzetta dello Sport says Bayer are exploring buying him back, with Salzburg aware of growing interest in the player.
Just 18, Salzburg are aiming to raise at least €20m this summer if they're to sell.
Alajbegovic's contract with Salzburg runs to 2029.