The Hammers were named instead of Tottenham as the preferred bidders by the Olympic Park Legacy Company (OPLC) in February.
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But a report in The Sunday Times then alleged an OPLC employee, Dionne Knight, worked for West Ham during the bidding process and was also in a relationship with a club executive, Ian Tompkins.
The newspaper's investigation was underpinned by information - in the form of bank and telephone records - provided by a private investigator, who was allegedly employed by Tottenham.
West Ham are working with the pol ice and the Information Commissioner's Office to ascertain whether this access to personal information breached the Data Protection Act.
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The club claimed on Wednesday night this 'constitutes serious criminal conduct'.
An OPLC spokesperson was unavailable for comment.
The organisation instructed an independent barrister in July to look at the consultancy work carried out by Ms Knight.
A separate independent investigation, carried out by auditing firm Moore Stephens, is currently looking into the OPLC's 'internal stadium procedures'.
A Metropolitan Police spokesman said: 'As we have said previously, we have confirmed that West Ham and the OPLC have made allegations to us in respect of illegally obtained information. Those allegations are under assessment, pending the OPLC's internal inquiry.'
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A Tottenham spokesman said last night the club were unable to make any comment as it is an ongoing legal matter.
West Ham have also claimed an independent investigation 'completely exonerates' the club of any wrongdoing regarding its successful bid for the Olympic Stadium and 'that Ms Knight's work had in no way affected the integrity of the joint West Ham United- London Borough of Newham bid, which was approved by the OPLC'.
West Ham confirmed on Wednesday that midfielder Luis Boa Morte, 33, has left the club by mutual consent to 'allow him to pursue opportunities abroad'.
The club are also understood to have given up their chase for Reading's Shane Long, with Leicester City understood to be favourites to sign the striker for around ?7million.
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