Off contract in June, the Argentina international is a target for several European giants, including Barcelona and Juventus.
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The Sun says Newcastle are also keen as they seek a top class centre-half signing this summer.
Bournemouth have made multiple attempts to secure Senesi to a new deal, but without success.
Newcastle boss Eddie Howe is a fan and Toon chiefs believe they have the spending power to compete with any club on the continent in terms of a Bosman battle.