The Togolese forward, on loan from Manchester City in 2011-12, notched an impressive tally of 18 goals as he helped to fire Harry Redknapp’s side into the top four.
And the 28-year-old has said that he will not “beg” to stay in north London but will always appreciate his time at the club.
“I don’t know yet whether I’ll be here or not next year but my first choice now would be to stay at Tottenham,” Adebayor told the London Evening Standard.
“I am not going to go on my knees and beg anyone; this is for others to sort out.
“If a deal can be done, then fine. I would love to play for Tottenham. If not, then trust me, I will keep Tottenham in my heart.
“I am a huge fan of Tottenham now and I love the club. If I am not at the club in the future, I will be following their games and wishing them luck.
“I played at Arsenal for three years but today I keep Tottenham in my heart more than Arsenal, even though I haven’t played here for as long.”
The former Gunners striker was instrumental in helping Spurs to almost guarantee Champions League football, but the side’s early-season title challenge came off the rails in the second half of the campaign.
“Our target was to finish in the top four but we could have done better,” Adebayor admitted.
“We played some great football but there was a point where a bit of tiredness kicked in and there were injuries to important players, like Aaron Lennon.
“I don’t know yet where I will be next season but the target has to be to make progress every year. Tottenham were fifth the season before this one, fourth this season, so it is time to try for the top three next year.
“I believe Tottenham are going to become a bigger club, one of the main contenders, but to do that, they have to be in the Champions League.”