Adebayor's early goalscoring record made him a cult hero at Arsenal, but he caused fury among Gunners fans by pleading for a move to Manchester City and then performing an outrageous goal celebration when playing for the Lancashire club against his former team-mates in 2009.
The striker's can expect an even more hostile reception from the Arsenal fans on Sunday, but Redknapp said: "There is always aggravation when players leave clubs but he will get on and hopefully play well."
Redknapp added: "William Gallas played against Arsenal last year and for me was the man of the match. He showed his character last year in that game and I am sure Manu will do the same on Sunday."
Redknapp's men are currently sixth in the Barclays Premier League after putting a poor start behind them to go on a three-match winning streak.
Arsenal have endured a miserable start to the season - they have only won two games - but the Spurs boss thinks it would be foolish to write off the Gunners' title chances so early.
Redknapp said: "I would not write Arsenal off. If you write Arsenal off in your newspaper you could be made to eat all those words.
"They are a good side with a great manager."
Source: PA
Source: PA