UPDATE 3-Generali chairman hopes Geronzi becomes his deputy

(Recasts with Generali chairman wanting Geronzi as his deputy, adds bylines)

By Gianluca Semeraro and Andrea Mandala

CERNOBBIO, Italy, Sept 5 (Reuters) - The chairman of Generali (GASI.MI) said he hopes Cesare Geronzi, chairman of the Italian insurer's biggest shareholder, will eventually also become Generali's vice-chairman.

Speculation that veteran Italian banker Geronzi could take up a such position at Generali has circulated since he announced plans to change the governance of investment bank Mediobanca that would reduce managers' independence and allow him in principle to gain the deputy seat at the insurer.

When asked what he thought about the possibility of Geronzi becoming vice-chairman of Europe's fourth-biggest insurer by size, Generali Chairman Antoine Bernheim said: "I hope so, but I'm not the one to decide, it's the board."

Speaking on the sidelines of a business conference on Friday, Bernheim said Geronzi, who leads the supervisory board at Mediobanca (MDBI.MI) which owns 15.7 percent of Generali, had a strong personality.

"I do not know what the word governance means but I do think that a company goes well if its managers are good and that it goes badly when managers are bad no matter its governance," Bernheim said.

Mediobanca's current governance structure forbids Geronzi from holding an executive position in a company in which the investment bank has a major stake, such as Generali.

This prohibition is expected to disappear if Geronzi succeeds in implementing his plan to change the bank's governance -- a dual-board system adopted last year that he says gives management too much power.

Geronzi said last summer that the rule was inspired by "the groundless fear that I wanted to become chairman or deputy chairman of Generali. I have no such a cravings."

NO CHANGES AT GENERALI

Bank UniCredit, Mediobanca's biggest shareholder with an 8.7 percent stake, has said that changes in the bylaw can only happen with the agreement of board members and management.

Unicredit Chief Executive Alessandro Profumo said changes to the bank's governance structure were needed but that timing was not important. Geronzi has said he wants the changes soon.

On Friday, Profumo, also attending the business conference on Lake Como, said work on the planned governance changes was going "positively."

"From what I know, they are working in a positive manner, we shall see," Profumo said on the sidelines of a UniCredit presentation of its industrial plan to advisers.

Earlier, Bernheim said he did not foresee any changes to the management structure at Generali, defending its own dual chief executive set-up.

The arrangement was criticised by Geronzi in August when he told Il Sole 24 Ore daily that the Generali chairman should have more power and the insurer's two chief executives less.

In the same interview Geronzi denied being interested in replacing Bernheim or becoming vice-chairman.

The 83-year old Bernheim rejected the idea of potential changes in Generali.

"We have ties with so many managers in so many countries that we need a chief executive to take care of them, and then we also need one for Italy," he said. "Two is the minimum to get things to work."

Activist fund Algebris has said Bernheim was too old for the job, also a criticism that Geronzi has made, and has called for a reform of its governance structure, arguing that its performance could be better. (Reporting by Gianluca Semeraro; editing by Will Waterman, Dave Zimmerman)