Adebayor, 28, a former Arsenal striker, has scored 18 goals in 37 games for Spurs since he moved to White Hart Lane on loan, helping the club to finish in the top four of the Premier League.
On Thursday, new Spurs manager Andre Villas-Boas revealed that the Togo international was high on his list of targets.
“It would be a lie if I tell you we are not looking for a striker,” Villas-Boas told reporters. “And of course Ade is part of that list. We are extremely willing to have Adebayor on board with us.”
The Togolese will become the club’s third signing for the new season.
Meanwhile, Dutch international midfielder Rafael van der Vaart said he was not leaving Tottenham despite speculation linking him with a possible return to Bundesliga side Hamburg, or a move to the United Arab Emirates.
“It’s incredible how my name has been mentioned in recent days in Europe,” van der Vaart told German daily Bild.
“I can only say these are rumours. I’ll probably play at Tottenham next season,” added the Dutch player who competed for Hamburg from 2005 to 2008.
Van der Vaart, 29, is under contract with Tottenham until 2014.