MILAN/LONDON (Reuters) - Guarantor UniCredit (>> UniCredit SpA) is considering whether to delay Banca Popolare di Vicenza's 1.76-billion euro (13.9 billion pounds) rights issue, currently slated in April, if market conditions do not improve, three sources close to the matter said.

Popolare di Vicenza must raise the cash and list on the Milan bourse to comply with European Central Bank (ECB) requests to boost its capital base.

The fund-raising is regarded as a crucial test of investor confidence in Italian banks, whose shares have sold off sharply this year because of concerns about 360 billion euros of bad loans clogging their balance sheets. Negative official interest rates are further squeezing euro zone banks' margins.

The sector turmoil has alarmed Prime Minister Renzi's government, which has been promoting mergers among cooperative banks and sought to speed up the sale of soured debts to strengthen the industry and kick-start lending to businesses.

"A delay is a possibility," one of the sources said, speaking on condition of anonymity because the issue is sensitive and no decision has been taken yet.

UniCredit has signed a preliminary contract to underwrite the cash call for up to 1.5 billion euros but can hardly afford to end up with a big stake in a weak bank, the sources said.

Italy's biggest bank by assets could also use a clause in the contract that allows it to back out of the underwriting deal in case of adverse market conditions, one of the sources said.

"No one guarantees anything if the market conditions are not right. UniCredit has no intention of becoming a shareholder in the bank," the source added.

A second source said the rights issue was likely to be postponed as industry valuations needed to rise. A delay would have to be cleared with the ECB, which declined to comment.

A source at Popolare di Vicenza said the capital raising plan was going according to schedule. The bank submitted a prospectus at the end of February and is waiting for approval from regulators, it said.

One of the sources also said a flurry of recent deals involving Italian banks could signal a change of sentiment and help the Popolare di Vicenza's cash call go through on schedule.

Banca Popolare di Milano (>> Banca Popolare di Milano) and Banco Popolare (>> Banco Popolare Societa Cooperativa) announced a much-anticipated merger last week, although that deal also includes a 1-billion euro capital increase to be undertaken by Banco Popolare.

Banca Carige (>> Banca Carige SpA) said on Tuesday U.S. fund Apollo (>> Apollo Global Management LLC) had offered to buy a controlling stake by acquiring the bulk of a 550-million euro share issue.

The Financial Times said on Wednesday that UniCredit was in talks with the government to drum up support for the rights issue. A treasury spokeswoman said: "The operation is going ahead, the government is monitoring but there is no cause for concern." UniCredit declined to comment on the report.

Regional peer Veneto Banca, which must also tap the market for 1 billion euros to comply with ECB requirements, has already postponed its own capital increase to May. The chief of Intesa Sanpaolo (>> Intesa Sanpaolo SpA), which is underwriting that rights issue, said on Wednesday the bank would fulfil its commitment.

(Additional reporting by Valentina Za; Writing by Silvia Aloisi; Editing by Ruth Pitchford)

By Paola Arosio and Pamela Barbaglia