MILAN, Feb 4 (Reuters) - Italy has sketched out a plan for a state-backed bad bank to mop up problematic loans of Italian lenders and strengthen their balance sheets, Italy's Il Messaggero newspaper said on Wednesday, citing a draft copy of the plan.

The plan, which is being put together by the Bank of Italy, the Treasury and the prime minister's office, is designed "to help the sale by banks of a significant part of their non-performing loans towards companies".

Bad loans, which stood at 181 billion euros ($208 billion) in November, are a major concern for Italy's lenders which fared the worst in a Europe-wide health check of the sector last year.

Italy is hoping its banks will be better able to lend to companies once risky loans have been taken off their books.

The bad bank, which would have capital of around 3 billion euros, would count among its shareholders state-lender Cassa Depositi e Prestiti, the Bank of Italy, the banks selling the loans and possibly private investors, Il Messaggero said.

According to the document called "New credit for growth", the state could take either a minority stake of 49 percent in the bad bank, which would mean it did not need to be booked as state debt, or a majority stake of 81 percent.

The plan, which has been mentioned to the European Central Bank, will be sent to Brussels when completed, Messaggero said.

Last month Economy Minister Pier Carlo Padoan said Italy was considering setting up a bad bank.

The Treasury declined to comment.

($1 = 0.8715 euros) (Reporting by Stephen Jewkes, additional reporting by Giselda Vagnoni; Editing by Toby Chopra)