The 19-year-old midfielder has come through the youth ranks at Brisbane Road and made his debut in late 2011.
Odubajo has since made rapid progress and has played over 50 games for the O's who tied him down to a new long-term deal earlier this year.
The speedy youngster, who can also play at full-back, is now generating a lot of interest and clubs from the Premier League and Championship are keeping close tabs on him.
It is understood Newcastle, Reading, Middlesbrough and Birmingham are amongst the clubs who have watched him in recent week.
His agent Hootan Ahmadi admitted interest was mounting, but insisted the player was happy with the progress he is making at Leyton Orient.
"Moses is doing very well, and it is no secret a number of clubs have been watching him," Ahmadi told Sky Sports.
"But he is also very happy at Orient and that is the main thing for a young footballer, to enjoy his football and progress."