Adds details from source in fourth paragraph

MILAN, June 17 (Reuters) - Leonardo Maria Del Vecchio is exploring private debt options to help finance a €10 billion ($11.6 billion) deal to increase his stake in family holding company Delfin, the top investor in EssilorLuxottica ESLX.PA, a source close to the Italian businessman said on Wednesday.

He currently holds a 12.5% stake in Delfin and aims to buy out the stakes of two siblings to raise it to 37.5%. He had been working on a financing package with banks UniCredit CRDI.MI, BNP Paribas BNPP.PA and Credit Agricole CAGR.PA.

The move to look at private debt comes as reaching a final agreement with the banks is taking longer than expected, the source added.

BNP Paribas has recently moved away from the deal, two sources said, while a third said the French lender had become more cautious on the buyout financing as several conditions it requested remained unmet.

BNP was not immediately available for comment.

Italian daily Il Sole 24 Ore reported on Wednesday that Del Vecchio is exploring alternative financing options, including contacts with U.S. fund Apollo Global Management APO.N .

Del Vecchio and Apollo declined to comment.

Leonardo Del Vecchio - the founder of the family business empire - died in 2022. In his will, he divided Delfin ​equally among his six children, as well as his widow and Rocco Basilico, her son from another marriage.

Del Vecchio is racing to close the deal with his siblings by the end of June, although negotiations are taking longer than expected over guarantees and legal disputes with Basilico, a third source said.

Del Vecchio and Basilico have reached a provisional agreement to settle an inheritance dispute and drop cross-lawsuits but a final agreement hasn't been reached yet.

Luxembourg-based Delfin owns 32.4% of Ray-Ban maker EssilorLuxottica and it is the largest shareholder in Italian lender Monte dei Paschi BMPS.MI with a 17.5% stake. It also holds 10.1% of insurer Assicurazioni Generali GASI.MI and roughly 2.8% of UniCredit CRDI.MI.

A meeting of Delfin shareholders is expected to take place on June 30, another source added.

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