The 28-year-old striker signed a permanent deal at White Hart Lane in the summer following a successful loan spell from Manchester City last season, but has found his chances limited to just four Premier League appearances so far this season.
And it is believed the Togo international is becoming increasingly frustrated at his lack of game time under new manager Andre Villas-Boas and is hoping for a move away in January.
La Liga side Celta Vigo are rumoured to be lining up an offer to give Adebayor a new start in Spain and improve their attacking options after netting just 11 goals in their opening 10 league fixtures.
But Atletico Madrid are also thought to be keeping tabs on the striker as they look to add to their impressive start to the season and fill the possible void left by top striker Radamel Falcao, who is the subject of increased speculation of a move away from the Vicente Calderon Stadium.
Meanwhile, Tottenham are thought to be competing with Liverpool for the signing of Schalke’s Dutch striker Klaas-Jan Huntelaar.
The 29-year-old striker, who scored against Arsenal in the Champions League last night, will be out of contract at the end of the season and Andre Villas-Boas is desperate to improve his attacking options and may see him as the perfect replacement for Adebayor.