MILAN, Dec 16 (Reuters) - John Elkann, scion of the Agnelli family, has tightened his grip on Giovanni Agnelli BV, the family holding that controls the industrial conglomerate Exor, Italian financial daily Il Sole 24 Ore reported on Saturday.

Exor is the single largest shareholder in automaker Stellantis and Dutch healthcare equipment maker Phillips. It also controls groups including Ferrari , truckmaker Iveco and football club Juventus .

Giovanni Agnelli BV is jointly held by 100 descendants of Fiat founder Giovanni Agnelli.

Through his family entity Dicembre, Elkann has bought around 3% of Giovanni Agnelli BV from his cousin Andrea Agnelli, raising his stake to almost 40% while Andrea cut his shareholding to nearly 9%, the newspaper said.

However, Andrea will represent John Elkann's stake on the board, the paper added.

New York-born Elkann is the CEO of Exor and the chairman of Stellantis and Ferrari. Late Fiat founder Gianni Agnelli was the grandfather of John.

One source close to Andrea Agnelli said that he does not plan to reduce his stake in the holding company further.

Earlier this year Andrea Agnelli, who is the former chairman of Juventus, left the board of directors of both Stellantis and Exor following a financial scandal at the club.

A representative for Elkann declined to comment. (Reporting by Francesca Landini, additional reporting by Giulio Piovaccari; editing by Clelia Oziel)