Adebayor has slipped down the pecking order at City and spent the second half of last season on loan at Spanish giants Real Madrid.
Real have hinted that they would like to bring the Togolese frontman back on a permanent basis, but Jose Mourinho is chasing a number of other targets.
That could allow Tottenham to steal a march on the Primera Liga outfit, with Redknapp having been a fan of Adebayor for some time.
He has turned out for Spurs' fierce north London rivals Arsenal in the past, but soured his relationship with the Gunners when he pushed through a move to City in 2009.
Redknapp would have no qualms about bringing the 27-year-old back to the capital and admits he has discussed the possibility of making a move during the summer transfer window.
Speaking on Spurs' pre-season tour of South Africa, he said: "The chairman, Daniel Levy, has been speaking about it, I am not sure if it will happen. He is a name that has certainly been mentioned, certainly.
"I spoke to the chairman about loaning the player and if we could work out a deal for him, I would like to bring him to the club."