The revelation comes despite Spurs getting the green light to build their own new £400million stadium at a special meeting held by Haringey Council.
Spurs chairman Daniel Levy said in a statement issued this morning: 'I can also confirm we have registered an interest in the Olympic Stadium site within the deadline of September 30, in conjunction with AEG (Europe), the world's largest entertainment and facilities management company.
Gazumped: An artist's impression of the Olympic Stadium that Spurs will fight West Ham to occupy
'It is only prudent and good management that we ensure that we investigate all possible options for the club. We were informed by the Olympic Park Legacy Company that were we not to register an interest at this time, there would not be an opportunity at any future date.
'We have always maintained that we wouldn't undertake any project that could undermine the overall financial stability and future success of the club and this shall remain our guiding principle going forward and in determining our best option in the interests of the club and all its fans and stakeholders.'
Spurs' preferred option appears to be to build a new stadium closer to their current north London home at White Hart Lane, and Levy was delighted at the news that their application for what is called the Northumberland Development Project was approved by Haringey Council.
Grand plans: Artists impression of the new Spurs stadium
'Clearly we are delighted with this unanimous decision and are grateful to all those who expressed such clear support for the plans,' he said.
'I should stress that there is still much work to be done. We shall continue to work with Haringey Council and the application will now be considered by the Mayor of London and referred to the Secretary of State.
'We shall keep everyone connected with the club updated over the coming months as discussions continue with the various public sector bodies.'
Match day: Spurs want top-class facilities
Planning permission has been granted to build the 56,250-seaterstadium, but the final decision rests with Boris Johnson, the Mayor ofLondon, who has to rubber-stamp the project within two weeks.
Spurs boss Harry Redknapp described the news as 'fantastic for the club' but said even he didn't know which stadium he would rather play at.
Asked which he would prefer, he said: 'I don't want to say the wrong one! And for Daniel to say, 'What's he talking about?".
VIDEO: Redknapp on stadium plan.'The new stadium would be great and the Olympic Stadium would be great.'
West Ham delivered their bid to run the Olympic Stadium after the 2012 Games to 10 Downing Street yesterday, insisting only they could deliver the legacy promise made when London was named host city.
Hammers players Scott Parker, Carlton Cole and Mark Noble took the joint proposal with Newham Council to the Prime Minister's residence after it was formally presented to the Olympic Park Legacy Company earlier in the day.
The plan would see the stadium's capacity reduced to 60,000 and it would host football and athletics, alongside other major sports, concerts and communityfacilities.
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