The Olympic Park Legacy Company (OPLC), which approved West Ham's bid ahead of Spurs last month, confirmed Tottenham had made formal enquiries ahead of a potential judicial review.
"We can confirm that a letter before action in relation to potential judicial review proceedings has been issued," the OPLC said in a statement.
"We are confident that if these judicial review proceedings are pursued, our approach will be entirely vindicated by the courts."
Tottenham informed the OPLC of a possible challenge this week as construction on the 80,000 seater Olympic Stadium, which has taken three years to build, was completed ahead of schedule.
"At this stage the club has not issued any proceedings against the Olympic Park Legacy Company or any other party in respect of the decision regarding the award of the Olympic Stadium," Tottenham said in a statement.
"The club's lawyers have written letters to the OPLC, the Mayor of London, the Minister of Sport and the Secretary of State for Local Government and a separate letter to the London Borough of Newham raising a number of concerns with the processes which led to the award.
"The letters also requested - in the interests of transparency - for the provision of certain information concerning the processes, which the club considers that it is entitled to.
"Tottenham Hotspur will determine its next step as and when it receives a response to these letters."
West Ham won the battle to inherit the Olympic Stadium in February.
The OPLC backed their plans for the venue ahead of Tottenham who wanted to demolish a large part of the 500 million pound stadium and rebuild it without a running track.
"The Olympic Park Legacy Company ran a very rigorous and transparent process in its selection of the recommended preferred bidder," the OPLC added in Wednesday's statement.
"We have been supported by independent experts in their field in terms of legal, financial, commercial and technical advice.
"We have been consistent, fair, objective and entirely equal in our dealings with the bidders from start to finish."
West Ham's bid, which plans to cut the capacity to 60,000 whilst retaining the track around the pitch, was endorsed by the International Olympic Committee which felt it honoured a commitment made when London was awarded the Games in 2005.
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