The Mirror says Llorente is on the Gunners' hit-list of possible January deals to boost their squad and push for the Premier League title.
Arsenal scouted Llorente before he joined Juve on a free last summer from Spain's Athletic Bilbao.
They have now been alerted to his potential availability.
Any transfer would almost certainly be a loan as Arsenal look for more long-term options, and may not want to make a big signing if they are already cup-tied for the Champions League.
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