The 7.5 billion euro ($9.7 billion) rights issue by UniCredit SpA
Take-up could be around 97 to 98 percent, a source close to the banking consortium handling the issue told Reuters. Subscriptions are expected to be at least 95 percent, another consortium source said.
Friday is the last day of trading in rights to the heavily discounted new shares.
Some 31 European banks must tell their national regulators by Friday how they plan to fill the 115 billion euro collective hole in their balance sheets as part of moves to tackle the continent's sovereign debt crisis.
UniCredit's cash call will allow the Italian lender's core Tier 1 capital adequacy ratio to rise above the target of 9 percent of risk-adjusted assets required by the European Banking Authority and almost entirely plug the second biggest capital shortfall in the region after Spain's Santander
The two-for-one share offer ends on January 27 and will dilute 2012 earnings per share by around 65 percent, according to analysts' estimates.
The bank's chief executive Federico Ghizzoni said on Wednesday he was confident the sale would be successful, although the company's share price has fallen by around 70 percent in the past year.
The existing shares were trading ex-rights down over 2 percent at 3.29 euros by 1140 GMT, with the right to buy two of the new shares at 1.943 euros trading down 5 percent at 2.59 euros
They seem to have pulled it off, but for the historic shareholders it's a killer, said Alessandro Capeccia, who manages 500 million euros at fund Azimut sgr and said he preferred UniCredit's high-yielding bonds to its shares.
According to other sources close to the underwriting consortium, the rights issue has drawn interest from U.S. institutional investors and from Nordic countries.
Some core shareholders have indicated they will not take up their rights including the Libyan central bank and the Libyan Investment Authority.
Looking ahead, Italy's largest bank by assets remains vulnerable to the country's sovereign debt woes, analysts say, with already low profitability further dented by the dilutive cash call and question marks hanging over its strategy.
Despite having the biggest international reach among Italian lenders, with operations in 22 countries and 950 billion euros in assets, UniCredit makes 42 percent of its revenues in its home market, compared with 25 percent in Germany, its second biggest cash earner.
It also has 40 billion euros of Italian government bonds on its books, accounting for 43 percent of its total exposure to sovereign debt.
This is an international lender whose core market happens to be Italy and whose exposure to Italian government debt is considerable, said Nicholas Spiro, managing director of consultant Spiro Sovereign Strategy.
Italy remains a proxy for euro zone risk and is likely to experience a severe recession this year; this has implications for the bank's plan to improve its profitability, he said.
UniCredit's shares have also borne the brunt of a market sell-off in Italian assets, with its theoretical ex-rights market capitalization now below 20 billion euros, a far cry from the 75 billion euros former chief executive Alessandro Profumo could boast of just four years ago after a buying spree in central and eastern Europe.
That acquisition drive turned UniCredit into the biggest lender in Austria and in several central and eastern European countries, and gave it the third spot in Germany. But at a price.
As Italy and its banks got sucked ever deeper into the debt crisis Ghizzoni revealed a 10.6 billion euro third-quarter loss in November due to big writedowns on the book value of those deals.
Ghizzoni has come under heavy criticism for waiting too long to launch the rights issue on January 9, and the initial market reaction to the steep discount offered was a disaster -- the stock plunged 45 percent in the space of four days.
But the shares then partially recovered. Analysts have said a 90-95 percent take-up by shareholders would be a good result, given current market conditions.
Analysts at DZ Bank, which has a sell recommendation on the stock, estimated UniCredit's return on equity after tax in 2012 would be 2.6 percent, compared with a median of 7.4 percent for its European peers.
And with Italy's economy likely to slide into a recession several analysts say the 3.8 billion-euro profit target for 2013 is too ambitious.
($1 = 0.7757 euros)
(Writing by Lisa Jucca and Stephen Jewkes; Editing by Will Waterman)