MILAN/ROME (Reuters) - Top management at Banca Monte dei Paschi di Siena is pressing to increase the ceiling on a possible rights issue to 2 billion euros ($2.66 billion) from 1 billion euros, two sources familiar with the situation told Reuters.

Italy's No.3 bank took 4.1 billion euros in state aid this year to stay afloat but the troubled lender may need more money to cope with a worsening economic scenario and repay the state.

The bank, which needs to present a restructuring plan to the European Commission by June 17 to gain its approval for February's state bailout, is also at the center of a judicial investigation into derivatives trades that forced it to book a loss of nearly 1 billion euros ($1.33 billion).

"The management wants to do it (increase the limit). Technically, the bank needs more cash," one of the sources said, speaking on condition of anonymity.

The second source said that "the capital hike could be 2 billion euros, not 1 billion".

It is not yet clear whether shareholders would back the proposal to increase the ceiling for the capital increase, the first source added.

Monte dei Paschi did not respond to requests for comment.

Shareholders at Monte dei Paschi gave the green light to a capital increase of up to 1 billion euros last year as part of a plan to repay state aid and boost the bank's capital base.

However, the bank's efforts to attract investors are not helped by its rules limiting voting rights to 4 percent for all shareholders apart from top investor Fondazione Monte dei Paschi, a not-for-profit foundation that owns 33.7 percent of the bank.

The bank's management wants to scrap the 4 percent limit, but Siena mayor Bruno Valentini said on Thursday that it should not rush to change rules on voting rights.

The city of Siena, which Valentini represents, has the power to appoint four out of 14 members on the governing council of Monte Paschi's main foundation shareholder. ($1 = 0.7519 euros)

(Reporting by Lisa Jucca and Stefano Bernabei; Editing by Stephen Jewkes and David Goodman)

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