MILAN, June 30 (Reuters) - Hedge fund Algebris Investments will emerge as one of the top shareholders in Fineco bank, controlled by Italy's No.1 lender UniCredit  
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   , following the online broker's initial public offering, Algebris CEO Davide Serra said on Monday.     Fineco, Europe's largest online broker, last week priced its IPO at 3.70 euros a share in an offer than was three times over-subscribed by investors.     The bank is due to debut on the Milan stock exchange this week, with an initial market capitalisation of 2.24 billion euros, Italy's second-biggest market listing so far this year.  
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         "We are going to emerge as one of the largest investors in Fineco," Serra told reporters on the sidelines of a conference in Milan. He decline to specify how large Algebris' stake in Fineco would be.     "Fineco is the best online bank in the world and has a fair fee system with regards to clients," he added.     Trying to capitalise on a more favourable investment sentiment towards southern Europe, a raft of Italian companies are tapping investors for cash through debt and share issues, including Banca Monte dei Paschi di Siena's successful 5-billion-euro capital increase that was concluded last week.     Serra said his fund had been in touch ahead of the cash call with the bank's top investor, a Siena-based charitable banking foundation, for a possible purchase of the foundation's stake in Monte dei Paschi, Italy's third-largest bank by branches.      Talks stalled, however on valuation, Serra said. He did not say whether Algebris, which specialises in investments in the financial services sector, had taken a stake in Monte dei Paschi as part of the bank's capital raising exercise.        (Reporting by Maria Pia Quaglia, writing by Lisa Jucca, editing by David Evans)  ((elisabetta.jucca@thomsonreuters.com)(Tel +39 02 66129442)(Reuters Messaging: elisabetta.jucca.thomsonreuters@reuters.net))  Keywords: FINECO ALGEBRIS/