The Federal Reserve Bank is taking a closer look at the U.S. units of Europe's biggest banks, concerned that a euro zone debt crisis could spill into the U.S. banking system, the Wall Street Journal reported.

The $2.5 trillion U.S. money market funds industry -- which supplies short-term dollar funding to banks -- has retreated from the euro zone in recent months, concerned that the continent's debt crisis is spiraling out of control.

That and the drying up of interbank lending has led to a trebling of dollar funding costs for euro zone banks in the last month. One bank was forced to borrow dollars at the European Central Bank on Wednesday.

In a dramatic shift, the U.S. branches of foreign banks became net borrowers of dollars from their overseas affiliates for the first time in a decade, Federal Reserve data released last week showed.

The Fed's New York branch -- which oversees U.S. units from many European banks -- is now asking for more information about whether the banks have reliable access to the funds needed to operate in the United States, the Wall Street Journal said.

New York Fed officials are very concerned about European banks facing funding difficulties in the United States, a senior executive at a major European bank who has participated in the talks told the Wall Street Journal.

The New York Fed was not available to comment.

On Wednesday, one euro zone bank borrowed $500 million from the European Central Bank at a rate much above those at which banks can get dollars in the open market. It was the first time since February 23 a bank used the central bank's facility.

Fed officials recently have held meetings with U.S.-based executives from top European banks to discuss their funding positions, the Wall Street Journal said.

Regulators are trying to guard against the possibility European banks that encounter trouble could siphon funds out of their U.S. arms, sources told the newspaper.

Regulators recently have ramped up pressure on European banks to transform their U.S. businesses into self-financed units to insulate them from problems at their parent companies, the WSJ cited a senior bank executive as saying.

French banks are most exposed to U.S. short-term funding, and it is access to U.S. dollar liquidity that is of particular concern. BNP's short-term borrowings were $94 billion and SocGen's were $56 billion, Citi analysts estimated last month.

European bank shares were 3.5 percent lower on Wednesday after hefty drops last week. But this time the fall was along with other sectors such as automobiles and construction shares, on concerns about global growth.

Franco-Belgian Dexia was hardest-hit, standing 8 percent lower at 6:09 a.m. EDT. The bank was the biggest borrower of the Federal Reserve's so-called discount window -- an emergency facility -- during the financial crisis.

(Reporting by Douwe Miedema and Steve Slater in London and Soham Chatterjee in Bangalore; Editing by David Cowell and Hans-Juergen Peters)