La Gazzetta dello Sport says Juve haven't dropped their interest in Greenwood, having been beaten by OM to his signing two summers ago when he was leaving Manchester United.
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Should OM miss Champions League qualification this season, they're expected to seek buyers for Greenwood, 24, to balance the books.
Juve intend to try again for the forward, who has scored 25 goals this season.
OM rate Greenwood at €50m, though that price could drop if Juve are willing to include Edon Zhegrova in their bid. The midfielder has been a long-target for OM.