The 19-year-old attacker has impressed head coach Mauricio Pochettino this summer and Spurs are keen for him to continue his development playing regular first-team football elsewhere.
Sources understand a number of teams from the Dutch Eredivisie have expressed an interest in taking the winger including AZ Alkmaar, Roda JC and Feyenoord.
Rangers manager Mark Warburton and Coventry boss Tony Mowbray, who both have strong relationships with Tottenham, have also expressed a desire to take Oduwa for a portion of next season and the player is hoping to play at the highest level he can.
Pochettino has identified Alex Pritchard, Harry Winks, Josh Onomah and Oduwa as the next wave of players who could make the first team, and Tottenham have been working to tie them all to new contracts.
Sky Sports reported in May that Pritchard has already been told he will be a fully integrated member of the first-team squad next season and has held talks over a new four-year contract.
Pritchard is expected to commit his future to the club while Onomah and Winks signed their new deals last month.
Oduwa signed for Tottenham in 2012 and has two England U18 caps. He is yet to make first team appearance and spent time on loan at Luton last season.