The 27-year-old Togo international spent the second half of last season on loan with Real Madrid in the Spanish Primera Liga after finding himself on the fringes of Roberto Mancini's first-team squad, behind the likes of Carlos Tevez, Mario Barlotelli and Edin Dzeko.
The former Arsenal forward was recently left behind in Manchester as City's first-team regulars departed for their pre-season tour of the United States, adding further fuel to the rumours that he is surplus to requirements at the Etihad Stadium.
Although Redknapp said he had discussed Adebayor with his chairman, Daniel Levy, he remained doubtful whether City would do business with one of their main rivals for a Champions League berth.
"He is a name that was mentioned and I spoke to the chairman about the player, about the possibility of loaning him, but whether they [City] would loan him I don't know," Redknapp told reporters in South Africa, where Spurs drew 1-1 with the Orlando Pirates in a pre-season friendly on Tuesday.
"If they would loan him we would be of interest. He is a quality player. We will wait and see."
With the news that Tevez's proposed move to Corinthians is off after the two clubs failed to negotiate the Argentine's transfer back to Brazil, Adebayor looks almost certain to be on the move before the close of the summer transfer window on September 1.
The African has talked up a return to the Bernabeu, where he scored five goals as he helped Jose Mourinho's side win the Copa del Rey last season, and has said previously he is prepared to wait until the 11th hour to secure a move back to the Spanish capital.
But with Real also linked with other high profile targets, such as Atletico Madrid's Sergio Aguero, Adebayor has now been linked with a move back to north London and Tottenham.
Meanwhile, Vincent Kompany is convinced Manchester City will be stronger in the new season - whether Tevez is still at the club or not.
It has been suggested that some City players have urged Mancini to strip Tevez of the captain's armband when he returns to the club following his involvement in the Copa America, where Argentina bowed out in the quarter-finals, with Kompany a more stable alternative.
That is not an issue Kompany wishes to consider.
"Whether he stays or goes, it won't change what we want to achieve," the Belgian central defender said. "The goals remain the same."
* Compiled by The National staff, with agencies