Assou-Ekotto has been one of Spurs' most consistent performers this season, helping the Londoners climb to fourth in the Barclays Premier League table with one match of the season remaining.
The Cameroon international, who joined the club in 2006, played in every one of the club's league games until he dislocated his shoulder against QPR last month.
Manager Harry Redknapp has constantly sang the full-back's praises, but it seems the 28-year-old could leave the club at the end of the season.
"Everything is possible," Assou-Ekotto told France Football.
"When I met my chairman last January, he told me that if a club bigger than Tottenham came for me, it (the club) would not necessarily be against a departure.
"With my chairman, there was a gentleman's agreement. As he is a man of his word, I hope it will make things easier if a great club comes in.
"If there is a change at Tottenham - some more money is made available maybe - I wouldn't be against the idea of staying, but otherwise I'll try to move forward, as I did when I left Lens."
In ordinary circumstances, Tottenham would be guaranteed a place in the Champions League if they ended the season in the fourth position they currently occupy.
But Chelsea's passage through to the Champions League final means Redknapp's team will only qualify for the Europa League if the Blues beat Bayern Munich on May 19 and Spurs fail to move ahead of Arsenal into third this weekend.
Assou-Ekotto, it appears, would not be content at a club who are not playing in Europe's premier competition next term.
"All players want to play this competition," he said.
"A few months ago, I said I never wanted to participate in the Europa League, because this competition is useless.
"If I have to leave Tottenham, it will be to join a club that makes the Champions League.
"Spain, Italy, Germany, wherever. The grass is green everywhere!"
Meanwhile, Redknapp has told Spurs he wants them to act "boldly" in the transfer market this summer.
The 65-year-old looks set to remain at White Hart Lane after missing out on the England job and hopes to sign up to three top-class players as well as hold on to the likes of Gareth Bale and Luka Modric, who have been attracting interest from Europe's top clubs.
Redknapp has been linked with highly-rated Lille midfielder Eden Hazard and Ajax's talented centre-half Jan Vertonghen.
Vertonghen has just one year left on his current deal and appears keen on a switch to the north London club.
The 25-year-old told De Telegraaf newspaper: "The board is asking for a large amount for a player who is only contracted for another year.
"I trust that Ajax and Spurs can turn water into wine and sort it out soon.
"I owe a lot to Ajax but I have always given my heart and soul.
"My appreciation for the club and fans is great and it would be terrible if my farewell was marred by Ajax sticking to a great price.
"Of course I want Ajax to gain financially but the amount Tottenham are willing to pay - perhaps with a little extra - is very reasonable.''
Vertonghen believes he would fit in nicely at Spurs, adding: "Tottenham is a fantastic football club.
"Ajax was the perfect club for me, but Spurs will be very close in nearing that already. They buy young, eager and offensive-minded players."