Newham Council has arranged a £40 million loan to finance West Ham's move to the stadium after the 2012 Games.
In a statement, Tottenham said: "The Club has today sought permission from the High Court to bring a claim against the London Borough of Newham ("Newham") for judicial review of Newham's process in providing a loan for the conversion of the Olympic Stadium after the 2012 Games."
The statement added: "The Club wrote to Newham asking it to explain its reasons and justification for its decision, but Newham has declined to respond to this request for information. Due to the time limits which apply to claims for judicial review, the Club has had no alternative but to issue these proceedings in order to protect its position.
"The Club continues to hold discussions with both local and national government bodies in order to seek to agree a feasible stadium solution."
Tottenham lost out in a head-to-head contest with West Ham to become the new tenant of the stadium in Stratford, east London.
West Ham, in a joint bid with Newham Council, intend to convert the 80,000-seater stadium into a 60,000-capacity facility which retains an athletics track. The club plans to move from Upton Park in 2014/15 with a 250-year lease and to give a 250-year lease to UK Athletics (UKA).
Tottenham's plans, part of a joint bid with AEG sport and entertainment group, had been to create a football-only stadium without the track and to redevelop Crystal Palace for athletics.
Source: PA
Source: PA