* Stake sale comes ahead of bigger than expected rights issue
* Fintech Advisory now Monte Paschi's biggest shareholder
* Monte Paschi increased size of rights issue to 5 bln euros (Adds details, shares)
MILAN, April 23 (Reuters) - Asset manager BlackRock has cut its stake in Monte dei Paschi di Siena less than a month after becoming the Italian bank's single biggest shareholder, raising questions over who will buy into the lender's imminent capital increase.
A regulatory filing on Wednesday showed that U.S. group BlackRock cut its stake in Italy's third-biggest bank to 3.23 percent from 5.75 pct on April 15, the day shares in Monte Paschi fell 10 percent on expectations that it would raise the size of its cash call.
A statement from the bank that day said it was evaluating its capital needs after a media report said that it may increase the size of its rights issue from a planned 3 billion euros ($4.14 billion).
Last Friday the bank's board approved an increase in the cash call to 5 billion euros as it strives to repay state aid and prepares for this year's stress tests on euro zone lenders. It expects to complete the rights issue by mid-July.
BlackRock bought Monte dei Paschi shares on March 18 from a banking foundation that was then the lender's top investor. It became the bank's leading shareholder at the end of last month as the foundation cut its holding further to repay debt.
The world's largest money manager has become a leading investor in several large Italian banks in recent weeks as cheap Italian banking stocks have attracted investors willing to bet on a tentative economic recovery and widespread reforms by new Prime Minister Matteo Renzi to boost growth.
BlackRock's stake sale, however, raises questions over the stability of such investments as a number of Italian lenders prepare to raise about 10 billion euros in cash from investors.
Banco Popolare is close to successfully completing a 1.5 billion euro rights issue, while Banca Carige must raise 800 million euros in the coming months and Banca Popolare di Milano 500 million euros.
Fintech Advisory, a U.S.-based investment fund owned by Mexican businessman David Martinez, is now Monte Paschi's top shareholder with a 4.5 percent holding it bought from the banking foundation.
The not-for-profit foundation has sold about 30 percent of Monte Paschi since the start of the year, leaving it with only a 2.5 percent stake.
Shares in Monte dei Paschi rose 3 percent by 1402 GMT after a rating upgrade to "neutral" by Goldman Sachs. ($1 = 0.7248 Euros)
(Reporting by Valentina Za and Francesca Landini; Editing by David Goodman)