Adebayor is out of favour at Manchester City and spent the second half of last season on loan at Real Madrid. He is training with the reserves after being left out of the squad for the pre-season tour to North America.
The player has admitted he would welcome a move back to the Spanish capital on a permanent basis but Redknapp is hoping he can tie up a loan deal for the 27-year-old from Togo.
Special reserve: Emmanuel Adebayor (right) trains with City's second string
The White Hart Lane boss, on a pre-season tour in South Africa, 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.
'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.'
Adebayor risked a hefty fine from his current employers last week when he refused to train with the youth team after being left out of the first-team squad for pre-season.
He felt 'insulted and disrespected' after learning of his omission by email, saying at the time: 'I don't know what I have done wrong.
Head boy: Emmanuel Adebaor scores from Real Madrid against Tottenham
'I get an email, out of the blue, on my holidays telling me I wasn't going on the tour and they told me I am not going to train with the first team.
'It's an insult to me to tell me I am now only fit to train with the reserves.'
The move could have cost Adebayor two weeks' wages, around ?300,000, but he backed down and joined the second string at Carrington.
Adebayor, who scored twice as Real beat Spurs 4-0 in the Champions League last season, joined Arsenal from Monaco in 2006 but damaged his relationship with Gunners fans when he joined City in 2009.
He ran the length of the pitch to celebrate in front of the Arsenal support after scoring against them for his new club and kicked out at former team-mate Robin van Persie.
Adebayor later apologised for his celebrations but he landed a three-match ban for his clash with Dutch striker Van Persie.
Flashpoint: City striker Adebayor angers the Arsenal fans in 2009
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