JERUSALEM, April 12 (Reuters) - Israeli police plan to question two businessmen abroad in connection with a investigation into Prime Minister Ehud Olmert over a 2005 bank privatisation, an Israeli newspaper said on Thursday.

The state prosecutor in January ordered a criminal investigation into Olmert to see if he promoted the interests of the two men during the sale of Bank Leumi while he was finance minister two years ago.

A national police spokesman said he could neither confirm or deny the report, published in Yedioth Ahronoth, Israel's biggest newspaper. The businessmen, described by media as Olmert's friends, reside in the United States and Australia.

Olmert has denied any wrongdoing in the case, as well as several others which he is being investigated for, including a 2004 real estate deal.

Yedioth quoted a police source as saying questioning the businessmen was "needed to put together the full picture of the evidential infrastructure in the investigation towards the anticipated investigation of the prime minister in the case."

Olmert's popularity, already hindered by his government's handling of last summer's Lebanon war, has plummeted amid the scandals. His centrist Kadima party won a 2006 election.

Police had also questioned Olmert on Tuesday in an investigation into suspected corruption within Israel's Tax Authority, although police said he was not a suspect.

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