Italy's third biggest bank Monte dei Paschi di Siena could propose getting rid of the current 4 percent cap on voting rights next week as it seeks to win EU approval for a 4.1 billion euro ($5.4 billion) state bailout, sources close to the matter said on Wednesday.

Monte dei Paschi's management has said the lifting of the voting rights ceiling is needed to make the bank more attractive to new shareholders and has been requested by both the Bank of Italy and the European Commission.

Monte Paschi's board may call an extraordinary shareholders' meeting to approve the change to its bylaws when it next gathers on June 11, the sources said.

The bank needs to present a restructuring plan to the European Commission by June 17 in order to obtain its approval for the state bailout it received in February, and is likely to press ahead with plans to scrap the voting rights ceiling before that date, the sources said.

"The hope is that the board meeting on the 11th will be the one where a shareholder meeting is called to abolish the 4 percent ceiling. It needs to be done by June 17," said one of the sources.

For the voting rights cap to be lifted, Monte dei Paschi needs to win the backing of its top shareholder - a charitable foundation with close ties to local politicians which has a stake of around 34 percent in the bank, enough to veto any unwanted move.

The foundation has not yet said whether it would vote in favour of scrapping the voting rights ceiling, but its current management backs the proposal, a second source said.

The shareholder meeting next week could take place before the EU Commission gives its response to Monte dei Paschi's restructuring plan, something that is expected to happen before the end of the summer, according to a third source.

Monte dei Paschi was forced to request a state bailout to plug a capital shortfall exacerbated by the euro zone debt crisis and loss-making derivatives trades.

It plans to launch a capital increase of 1 billion euros next year aimed at new investors to bolster its finances.

Chairman Alessandro Profumo said last month lifting the voting rights cap was needed to persuade new shareholders to buy into the cash call.

($1 = 0.7642 euros)

(additional reporting by Silvia Aloisi in Milan, Francesco Guarascio in Brussels)