The young Israel international is being scouted by Villa ahead of the summer market.
Gloukh, 19, is also on the radar of Arsenal.
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The Express & Star says Villa boss Unai Emery is a fan and would welcome Gloukh's arrival as a potential replacement for Galatasaray loanee Nicolo Zaniolo.
Gloukh has a deal to 2027 with Salzburg, which rate him at 30m.