Many of them were not convinced the Togolese striker was the man to lead the line for the 'Spurs on a long-term basis when he signed a permanent deal in the summer of 2012.
There was also a perception that Adebayor raised his game only when a new contract was in the offing, or when in the shop window for other clubs while on loan.
He has done very little to disprove these statements during his time at Tottenham.
During his stint on loan at the club in the 2011-12 season, when his parent club Manchester City continued to pay part of his huge wage packet, Adebayor scored 17 league goals in 33 appearances, a ratio better than a goal per game.
That summer, manager Harry Redknapp was replaced by Andre Villas-Boas and the 'Spurs started the season with Jermain Defoe and Harry Kane as their only striking options.
Fans hoping for a star striker to be signed before the close of the transfer window could be forgiven for not having celebrated the arrivals of Adebayor and American Clint Dempsey.
As the 'Spurs met Adebayor's wage demands and signed him on a permanent basis, after a likely failure to sign other targets, he seemed confident he would repay their faith, the Daily Mail reported.
He tweeted: "I'm back!!! Tottenham here I come!! I'm hungry for goals...Get ready."
But it turned out to be a poor season for Adebayor.
He scored just five league goals, justifying the concerns of fans over his suitability for a permanent deal, as well as worries regarding his desire and work-rate.
By the time he scored a spectacular goal against Chelsea in the third-last game of the season, some of those fans had lost patience with him.
A move did not materialise, and on returning for pre-season training, the 29-year-old was made to feel surplus to requirements.
He was ordered to train with the reserves.
Adebayor has since returned to training with the first team, though there has been no suggestion he will dislodge Defoe or Soldado in the starting side.
Until today, that is, with speculation emerging that he will be given a chance at Sheriff Tiraspol in the Europa League tomorrow.
Does Adebayor deserve this chance? Should an impressive display earn him the right to compete with the other strikers for a place in the league lineup? Many 'Spurs fans will need some convincing.