MILAN/ABU DHABI, Jan 11 (Reuters) - Abu Dhabi investor Aabar Investments is set to buy more shares in UniCredit CRDI.MI in the Italian bank's upcoming 13 billion-euro ($14 billion) share offer, Italy's biggest ever cash call, three sources said on Wednesday.

UniCredit, the country's largest bank by assets, will launch the share offer next month to boost its capital base as it embarks on a restructuring plan under new CEO Jean Pierre Mustier.

UniCredit has already found a group of banks ready to mop up any unsold shares, unlike rival Monte dei Paschi di Siena BMPS.MI which last month had to be rescued by Italy's government after failing to find buyers for its stock.

A successful capital raising would be an important sign of market confidence in Italy's battered banking system, weighed down by bad loans and low profitability.

Mustier last month unveiled a plan to shift 17.7 billion euros in bad debts off UniCredit's balance sheet, cut 14,000 jobs and close 944 branches by the end of 2019.

One of the three sources familiar with the matter said Aabar had confidence in UniCredit's strategy and would buy new shares to keep its stake unchanged.

Given the cash call's size, Aabar would need to invest around 650 million euros to maintain its 5 percent stake that makes it UniCredit's second-biggest shareholder behind U.S. investor Capital Research and Management Company.

Aabar and UniCredit declined to comment.

A fourth source said on Wednesday the bank was set to launch its capital increase soon after approving full-year earnings on Feb. 9.

Separately, two sources confirmed a report in daily Il Messaggero saying the bank could sell new shares at a 30-40 percent discount to the theoretical price of the stock when excluding subscription rights.

The new shares could be sold at around 1.2-1.3 euros each before a planned reverse stock split, the sources said, adding however the bank had made no final decision on pricing yet.

By 1219 GMT shares in UniCredit fell 2.5 percent to 2.61 euros.

Mustier, a French investment banker formerly at Societe Generale, arrived at UniCredit in July to oversee a capital strengthening and a streamlining of its operations after capital worries had dogged the Italian bank for years.

He immediately started selling assets including Polish subsidiary Bank Pekao PEO.WA and asset manager Pioneer Investments.

The possibility that a slimmed-down UniCredit could become a takeover target has raised alarm in Rome after France's Vivendi VIV.PA became the top investor in former monopolist Telecom Italia TLIT.MI and aggressively built a large stake in broadcaster Mediaset MS.MI .

Both UniCredit and Societe Generale SOGN.PA in November declined to comment on rumours of a possible merger.

The head of the Lower House Budget Committee Francesco Boccia on Wednesday told Radio24 there was a French plan to take over UniCredit.

"There is a design to make UniCredit French," Boccia said.

One of the sources familiar with UniCredit's share issue said a merger deal for the bank was a concrete possibility once Mustier had completed his job. ($1 = 0.9505 euros)

(Writing by Valentina Za; Editing by Greg Mahlich) ((valentina.za@thomsonreuters.com; +39 02 6612 9526;))