Investors flush with cheap European Central Bank funds are expected to help Italy raise up to six billion euros at a bond auction on Wednesday and bring the nation's three-year borrowing costs below 3 percent, half what it had to pay a few months ago.

Relief at Greece's successful debt restructuring is also set to sustain a rally that has brought Italian short-term yields back to levels last seen long before the country began to be buffetted by the euro zone debt crisis in July.

Italy aims to sell up to 5 billion euros (4.1 billion pounds) of a new three-year BTP bond maturing in March 2015. In a sign of easing market pressure on the euro zone's third-largest economy, the Treasury has set the coupon on the new issue at 2.5 percent.

That compares to a 6 percent coupon on a three-year BTP bond Italy launched in late November, when it came close to following Greece, Ireland and Portugal into a scramble for emergency aid that could have become prohibitively expensive for Europe.

Market concerns have eased since then, aided by the ECB's decision to provide banks with unlimited three-year funds and the appointment of a reform-oriented government in Rome.

UniCredit analysts expect Italy's three-year debt costs to fall to around 2.8 percent on Wednesday - roughly in line with where the new bond traded informally on the eve of the auction - from 3.4 percent at a previous sale in mid-February.

Clearly there is interest for this segment of the curve, as Tuesday's bill auction also shows, said UniCredit's strategist Luca Cazzulani. With a fair value yield of 2.7 percent, the new BTP in our view offers a really good opportunity considering a cost of liquidity (from the ECB) of 1 percent.

Italy paid only 1.4 percent to sell one-year debt on Tuesday, the cheapest yield on this maturity since August 2010.

It will also sell an off-the-run September 2019 bond for up to 1 billion euros on Wednesday.

The challenge for Rome is to attract enough interest also on longer maturities, where economic fundamentals play a bigger role and foreign buyers account for a larger share of demand. Italy is already in recession and the Bank of Italy expects the economy to shrink up to 1.5 percent this year.

Rome faces bond redemptions worth 54 billion euros in March and April alone. It has met so far slightly more than a fifth of an estimated target of 215 billion euros for bond issuance this year.

(Reporting by Valentina Za; Editing by Ruth Pitchford)