Spurs could move level with second-placed Manchester United and just three behind Manchester City if they win the game in hand, which was rearranged from the opening day of the new season on August 13 following civil unrest which had started just yards from White Hart Lane after peaceful protests about the police killing of 29-year-old local man Mark Duggan and then swept across the country.
Like all clubs, Tottenham have a strong sense of community spirit. Redknapp, 64, grew up in London's East End, and the former West Ham boss feels the modern game can learn lessons from the past.
He said: "Hopefully we can still keep doing things in the community, all football clubs really. I think we should be getting back into the schools in the afternoons with the kids.
"I would like to see the players do it, and I would certainly do it, spend a couple of hours there.
"When I was at West Ham, [manager] Ron Greenwood got us all coaching the kids in the schools, we used to do four or five afternoons a week in Canning Town and West Ham.
"We all loved it and that is how we all got into coaching really. "The players would do it and it would be great for the kids, to bring them something to look forward to.
"I went to a rough old school, but the highlight of our week was having Clive Allen's dad, Les, coming in to take us for football."
Midfielder Scott Parker (knee) remains a doubt for Wednesday's clash. Centre-half Ledley King (hamstring) is also not match fit. Defender William Gallas and midfielder Sandro are once again out with calf strains.
Everton manager David Moyes admits it is "sad" his club have not been able to keep pace with the progress made by Tottenham.
The Scot believes Harry Redknapp's side are genuine title contenders, but remembers a time not so long ago when the two clubs were battling it out for European qualification.
But while Tottenham have built on their Champions League debut last season and can move within three points of Barclays Premier League leaders Manchester City with a win on Wednesday, Everton are mid-table and 18 points behind their hosts. And Moyes knows counterpart Harry Redknapp has benefited from having access to one thing he has not - money.
"It is a little bit sad they are starting to pull away from us a little bit more than I would like," Moyes said.
"I think it was only three or four years ago us and Tottenham were competing neck-and-neck for European places.
"It is frustrating because all managers will tell you when you are close and competing with teams you never like to see them go away from you, but we are looking at them going away from us at this present time.
"They have continued to kick on and over the years they have got in some really good players. Rafael Van der Vaart is one and Scott Parker another recently. "Tottenham, arguably, might be the biggest spenders in the Premier League - they have always supported whoever the manager has been.
"Football will always come back around sometime and some day hopefully they will be looking at the back of us. "At the moment it unfortunately looks as if you need a bit of finance to get it back, but it would be nice to think we could do it the way we have done it.
"We will work really hard and try to bring in players, produce our own players here, work with them, develop them and try to make them better. "That is how we do it at Everton, we don't do it any other way."
Midfielder Seamus Coleman is Everton's latest injury doubt. The Irishman limped out of the FA Cup victory over Tamworth to join the growing ranks of injured players.
Phil Jagielka (knee), Leon Osman (foot), Jack Rodwell (hamstring), Tony Hibbert (groin), Tim Cahill (groin) and Ross Barkley (knee) were absent on Saturday and all six are likely to be missing again.
Tottenham V Everton - view commentary, squad, and statictics of the game live.