Adebayor was heavily criticised two years ago when he ran the length of the pitch to celebrate in front of the Arsenal fans after he scored against them for Manchester City.
Already an unpopular figure for leaving for the Lancashire club, the incident made Adebayor a hate figure among some sections of the Gunners support.
Adebayor was constantly heckled by Arsenal fans that afternoon at the Etihad Stadium - and the booing and taunts are likely to be even greater in number at White Hart Lane this weekend given that the 27-year-old now plays for Arsenal's bitter north London rivals Spurs.
Adebayor will be confident of scoring against Arsenal given that he has scored three times in three matches since signing on loan from Manchester City.
Redknapp feels he has no need to talk to Adebayor about any potential goal-scoring celebrations this weekend and is confident that his star striker will not go over the top if he does.
The Spurs boss said: "I'm sure he won't over-react again. I think he apologised last time. He's got a lot of respect for Arsenal still but he loves it here now, he's a Tottenham player.
"I've never spoken to him about it. I hope he does score a couple of times. I hope he slides on his knees and celebrates.
"I am sure he's going to get plenty of abuse come the weekend but he has just got to get on with his game.
"You can't react to that. He's got to get on with it. Fans are entitled to give players all the stick in the world so long as it's in the bounds of decency."
Today marks the 15th anniversary of Arsene Wenger's appointment as Arsenal manager, but if his team's recent form is anything to go by, there is not much reason for the Frenchman to celebrate.
Rocked by the departure of Cesc Fabregas and Samir Nasri this summer, Wenger saw his team put in their worst start to a season in 58 years.
They lost to Liverpool at home, Blackburn away and endured the humiliation of an 8-2 hammering at Old Trafford, although they have rallied somewhat with wins over Swansea and Bolton.
Some Arsenal fans have called for Wenger to go, but sacking the man who has brought three Barclays Premier League titles to the club since he moved from Japan would be foolish, Redknapp says.
"You know what it's like in football. You lose a few games and suddenly Arsene Wenger's a poor manager," Redknapp said.
"The man's been a great manager at Arsenal and I am sure he will be for many years to come. God knows what people are saying about him on the radio.
"They have had injuries. That has been the problem. I think the centre half (Thomas) Vermaelen is top drawer.
"They have missed him. I think he is a fantastic player."
Unlike Arsenal, Tottenham managed to hold on to their most-wanted player, Luka Modric, this summer despite Chelsea's interest.
However, that did not stop Spurs from losing their first two games - the second of which was an embarrassing 5-1 home defeat to Manchester City.
Redknapp's team have picked up since then, recording three straight league wins thanks partly to a shrinking injury list and the signings of Scott Parker and Adebayor.
Redknapp has only lost one of six north London derby meetings in the league since taking over and he is confident about taking all three points this weekend.
"They'll be difficult to beat but we are a very good team as well so I fancy our chances against anybody," the 64-year-old said.
"I am confident in my own team. I just feel we have good players here.
"Scott Parker and Adebayor coming in have made a massive difference to us.
"Sandro coming back from his long-term injury gives us strength.
"He's a fantastic player so we look strong."