MILAN (Reuters) - Veteran Italian banker Corrado Passera is presenting to the board of Monte dei Paschi <BMPS.MI> an alternative rescue plan which is backed by some U.S. private equity funds and sponsored by Swiss bank UBS <UBSG.S>, a source close to the matter said.

The board of the Tuscan bank met on Friday to approve first-half results and a rescue plan that envisages a 5 billion euro ($5.6 billion) share issue as well as a 10 billion euro sale of loans the bank granted to borrowers now deemed insolvent.

In a surprise statement on Thursday night, Monte dei Paschi said it had received two letters from UBS and former Italian Industry Minister Corrado Passera, without disclosing details about their content.

The source said the alternative plan envisaged a 2.5-3.0 billion euro cash call and the voluntary partial conversion of some of the bank's subordinated bonds into equity.

The new proposal includes the bad loan sale to Italian bank rescue fund Atlante, like the bank's own rescue plan.

Similarly, it also requires the European Central Bank to exempt Monte dei Paschi from having to revise its internal risk models following the bad loan sale, the source said. A revision would have a negative impact on capital.

(Reporting by Paola Arosio, writing by Valentina Za, editing by Emilio Parodi)