The 20-year-old spent last season with Orient in League One and is regarded as one of the top players in England’s third tier.
Odubajo has been linked to several other big name clubs recently, and nearly moved to Brighton back in January, but ended up signing a two-year contract with with the London club in March.
Tottenham were linked with Odubajo last October but nothing materialised, leaving the youngster to star for Orient as they missed out on promotion to the Championship in a penalty shoot-out against Rotherham in the play-off final.
He improved dramatically last season, his second, as he notched 12 goals in 57 appearances after scoring just three in 54 matches the previous season.
Tottenham are preparing for their first season under new boss Mauricio Pochettino, who takes over for Tim Sherwood, hired on an interim basis last season following the mid-season sacking of Andres Villas Boas.
Pochettino is expected to be active on the transfer market at White Hart Lane this summer as he hopes to bolster aSpurs squad that finished sixth in the Premier League last season.
The North London outfit have recently been linked with moves for several players, including Manchester United striker Javier Hernandez.