The Daily Mail is reporting that Arsenal boss Unai Emery is hoping to get a deal for the 19-year-old over the line.
The same article states that Emery is convinced Kean can end up having as big an impact on Arsenal as Thierry Henry.
According to the same story, Juventus would be open to selling Kean if they received a bid in the region of €35m (£31.5m).
However, the Daily Mail go on to add that Juventus would want to a buy-back clause to be included in any deal, or else Arsenal will need increase their offer to €40m (£36m).
The report reveals that Everton are prepared to rival Arsenal for the Juventus starlet and could have an advantage over their Premier League rivals given their openness to including a buyback clause.
Arsenal finished in fifth place in the Premier League table last season after the Gunners missed out on a Champions League spot.
The Gunners lost 4-1 to bitter rivals Chelsea FC in the Europa League final in Baku at the end of May.
Emery has only signed Brazilian teenager Gabriel Martinelli in a £1.6m deal from Ituano earlier this month.
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