Adebayor fell out with City boss Roberto Mancini last season and the Italian has made it clear the £25million striker has no future at the club.
Spurs and City have been in negotiations for some time over a deal, with Adebayor's reported £170,000-a-week wage packet proving to be the only real stumbling block.
Redknapp, who is preparing for tomorrow's Europa League clash with Hearts, hopes both clubs can overcome that hurdle as soon as possible, and there is the possibility that the 27-year-old, who spent three and a half years at Arsenal, could turn out for Spurs against Manchester United on Monday.
Redknapp said: "The chairman is talking to Man City about the player but where they (the negotiations) are at, I genuinely don't know. We will wait and see."
While the former Togo international has been a controversial figure at times during his time in the Premier League, his ability to score goals has never been in doubt.
The towering striker scored 46 goals in 104 appearances for the Gunners and Redknapp saw how lethal he is last season when he scored twice against Tottenham for Real Madrid in the Champions League quarter-final first leg clash between the two teams at the Bernabeu.
Spurs fans chanted abusive songs at the former Arsenal marksman during that match, but the player himself said this summer the songs would not put him off signing for Redknapp's team and he is not the first player to turn out for both north London teams.
David Bentley started his career at Arsenal but is currently in the Spurs squad, and William Gallas quickly became a fans' favourite when he moved to White Hart Lane from Arsenal last year.
Redknapp, who has been linked with a number of strikers this summer, was in Twente to watch Costa Rica international Bryan Ruiz last night but a deal for the player now looks unlikely, with the Spurs boss more worried about bolstering his midfield after a recent spate of injuries.
"He is a good player but we are more desperate in other areas," said Redknapp, who was speaking ahead of the play-off first leg against Hearts at Tynecastle.
"I don't think anything is going to happen."
Should Adebayor arrive, he is unlikely to be Redknapp's last summer signing.
Injuries to Sandro, Steven Pienaar, Wilson Palacios, Luka Modric, Tom Huddlestone and Jermaine Jenas mean Redknapp is short in midfield and moves for Lassana Diarra, Scott Parker or Thomas Hitzlsperger, who is training with the club after being released by West Ham, are possible.
Redknapp saw his side miss out on a Champions League place last year and fears the same may happen this year if new faces are not added due to the big-spending antics of rivals Liverpool and Manchester City.
"I want to get back in the Champions League but that's going to be difficult because three places are already taken probably. I can see a scrap between ourselves, Arsenal and Liverpool.
"We do need to get one or two in there if we are going to challenge."
Redknapp again rebuffed talk of Luka Modric, who misses tomorrow's game with a groin injury, leaving for Chelsea.
"I don't know where it's at and (chairman) Daniel (Levy) has said all along that he is not going to sell Luka so that is probably it as far as I know," Redknapp added.
"There is no sign of him going."
Despite his team being overwhelming favourites for tomorrow's game in Edinburgh, Redknapp expects the Scottish Premier League team to pose his side some questions.
"It will be a very tough game," Redknapp said.
"They are not a bad side and it's a difficult stadium to go to. It will be an intimidating place with a full house."