The 28-year-old, who first moved to the Premier League with Spurs’ north London rivals Arsenal in 2006, scored twice against Bolton Wanderers in a 4-1 victory at the Reebok on Wednesday night.
Adebayor’s brace took his tally to 16 goals for the season but the Togo striker is set to return to City at the end of the campaign.
But Redknapp is eager to bring Adebayor, who has previously played for Monaco and Real Madrid, to Tottenham on a long-term deal this summer.
“Of course I would [sign him]. I love Adebayor. He’s a real character and a good player,” Redknapp told the BBC.
“We’ll see what the summer holds. I’ve not spoken to the chairman yet, Daniel Levy has been busy, but when he gets back we’ll sit down and have a chat, but Adebayor has done very well for us.”
Redknapp has also been linked with a move for Belgian defender Jan Vertonghen, who is the current captain at Ajax.
And the 64-year-old admits he has watched the 25-year-old in action but Spurs are yet to contact the Dutch club with an offer for their skipper.
“He’s a player I’ve watched, he’s a very good player,” added Redknapp.
“But there are lots of clubs interested in him. We’ve not spoken to the club, he’s just a player I’ve watched along with loads of other players this year.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news