The 20-year-old is reportedly a top transfer target for the north London side this summer, as they try to prise the Belgian - currently on loan at Everton - away from Stamford Bridge.
But Lukaku is said to have already sparked Tottenham's interest before the current campaign, with the club offering 30-year-old Adebayor to the Blues in return for the young striker's services.
Spurs' interest could have stemmed from then manager Andre Villas-Boas, who was in charge at Chelsea when Lukaku moved to west London in the first place.
However, the duo have enjoyed a frosty relationship ever since. Most recently, Lukaku collided with Tottenham goalkeeper Hugo Lloris during Spurs' Premier League encounter with Everton, while AVB subsequently suggested he could have avoided the Frenchman during the clash.
Had Spurs signed the 20-year-old, though, they may not have invested in Roberto Soldado, with Lukaku's 11 goals in 22 league games proving, with hindsight, a much better return than Soldado's six in 25.
But would the club have been better off without Adebayor? It is no surprise that Villas-Boas, who forced the Togolese forward to train with Tottenham's youth team, would have wanted him out - but he has been a vital player for the club since his return to the first team under Tim Sherwood.
Adebayor has scored eight in 15 and, along with Denmark midfielder Christian Eriksen, has looked one of Tottenham's only bright spark in recent weeks.
Whether Chelsea will be open to letting Lukaku go is unclear, though the club have previously stated that they expect the Belgian to return to Stamford Bridge next season.
Would the Blues, meanwhile, have been happy with Adebayor as a replacement? Jose Mourinho has worked with the 30-year-old (at Real Madrid) before, while Samuel Eto'o is the only Chelsea striker to have equalled Adebayor's goal tally - having played four games more.