Police spokesman Mickey Rosenfeld said the evidence had been gathered in late December during a police raid on a house in Israel which is owned by the family of Austrian financier Martin Schlaff.
"On December 22, 2005, the national police investigation unit searched Schlaff's house (in Israel) and confiscated documents, paperwork, phones and his computers," Mr Rosenfeld said.
"We suspect that there could be proof within Schlaff'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 Mr Schlaff's lawyers, Mr Rosenfeld said.
"Since December 22, the national unit for investigations has not been able to confirm these suspicions after Schlaff turned to the courts who have temporarily denied police access to Schlaff's computer data," he said.
An Austrian Jewish investor, Martin Schlaff is one of the main owners of the Oasis Casino in the West Bank city of Jericho, which has been closed since the start of the Palestinian uprising five years ago.
The bribe is thought to be connected to a long-running corruption scandal which has plagued the Sharon family over illegal campaign contributions during the 1999 elections.
Officials in Mr Sharon's office refused to comment on the report, which was first broadcast late Tuesday by Israel’s 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.
The money is thought to be linked to an unresolved corruption scandal in which Mr Sharon was suspected of receiving a US$1.5 million (A$2.02 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 one of Mr Sharon's sons, Omri, 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 Sharon, who pleaded guilty to the charges in November, is due to be sentenced on January 23.