Off contract in June, the Argentina international is attracting interest from Europe's biggest clubs.
Barcelona are keen, with Juve also drawing up plans for the defender, says Tuttosport.
Juve are prepared to sell Lloyd Kelly at the end of the season, while fellow central defender Fede Gatti is wanted by AC Milan this month.
Juve know they're competing with Barca for Senesi and so are seeking pre-contract negotiations immediately.
Juve chiefs aim to convince Senesi with guarantees of better playing opportunities and a higher status in the dressing room compared to what Barca can offer.