Chairman and co-owner Dmitry Rybololev has identified the striker as a summer target despite the fact he is yet to appoint a new manager following Claudio Ranieri’s departure.
Tottenham, however, will not make a decision on Adebayor’s future until a new manager has been appointed.
Adebayor, 30, spent three years at Monaco before leaving for Arsenal in 2006.
Spurs are waiting until after Saturday’s Champions League final to see if there is a chance of luring Real Madrid manager Carlo Ancelotti to White Hart Lane next season.
If not, then chairman Daniel Levy will press ahead with plans to appoint Southampton manager Mauricio Pochettino, who has been offered a new three-year-deal to stay at St Mary’s.