Mickey Rosenfeld, the police spokesman told AFP on Tuesday, the evidence had been gathered in late December during a police raid of Martin Shlaff, an Austrian financer's family house in Israel.
Rosenfeld said: "On 22 December, 2005, the national police investigation unit searched Shlaff's house (in Israel) and confiscated documents, paperwork, phones and his computers.
"We suspect that there could be proof within Shlaff's computer data that the sum of three million dollars was transferred to the Sharon family."
However, although the police have actual possession of the computer hardware, they have been prevented from examining the data by a temporary court order issued after an appeal by Shlaff's lawyers, Rosenfeld said.
"Since 22 December, the national unit for investigations has not been able to confirm these suspicions after Shlaff turned to the courts who have temporarily denied police access to Shlaff's computer data."
The bribe is thought to be connected to a long-running corruption scandal which has plagued the family of Ariel Sharon over illegal campaign contributions during the 1999 elections.
Officials in Prime Minister Sharon's office refused to comment on the report, which was first broadcast late on Tuesday by private Channel 10 television.
Channel 10 showed footage of a police document which had been presented to a Tel Aviv district court in which it outlined evidence of the alleged bribe.
Omri Sharon pleaded guilty to
charges of falsifying documents
The money is thought to be linked to an unresolved corruption scandal in which Sharon was suspected of receiving a $1.5 million loan from South African businessman Cyril Kern that was allegedly used to refund contributions to his 1999 leadership campaign after they were deemed irregular.
The news came just hours after Omri, one of Sharon's sons, resigned from parliament ahead of his sentencing for providing false testimony and falsifying documents in a case linked to the financing of one of his father's leadership campaigns.
Omri, who pleaded guilty to the charges in November, is due to be sentenced on 23 January.