The veteran comes off contract in June.
Ole says the Uruguayan forward has made up his mind to join Boca Juniors in the summer and see out his career with the club, fulfilling a lifelong dream as he does so.
Boca are still skippered by the former United forward Carlos Tevez, but the 37-year-old could be replaced in Buenos Aires by Cavani, who is three years his junior.
Cavani has already spoken to Boca Juniors president Juan Roman Riquelme, and made clear that he wants to end his days in Europe in order to join his boyhood club.
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