With Premier League leaders and holders Manchester City ousted in the third round by Manchester United, who were then knocked out by Liverpool in the next round, Redknapp's men are strongly fancied to win a first FA Cup since 1991.
Spurs make the short trip to the League One side whose reward for reaching the fifth round of the competition for the first time is a meeting with the big boys.
There is already one real circus in residence in Stevenage and on Sunday there will be a metaphorical one when Spurs fans, vocal in their pleas to Redknapp to stay with the club rather than fill the vacant England job, come to town.
Redknapp, who was last week cleared of tax evasion by a court, is being persistently linked with the national team post and last weekend's 5-0 thumping of Newcastle United in the Premier League did nothing to quieten the calls.
Third in the league behind the two Manchester clubs, Spurs could be tempted to give some of their bigger names a rest before their North London derby against Arsenal the following weekend but that will not dampen excitement around Stevenage.
"There is a fantastic feeling. The feeling around club is so good," Stevenage Chief Executive Bob Makin was quoted by local media as saying.
There were queues around the block as home fans tried to get their hands on tickets for the visit of top-flight opposition and giant-killing dreams were indulged as supporters posed for photos with the FA Cup in the town 30 miles north of London.
It is a familiar place for Spurs, whose reserve team used to play in Stevenage and who have plenty of fans living there, but there will be no room for sentiment as seven of the eight games feature Premier League sides against lower division opposition.
The only all top-flight game is Arsenal's trip to Sunderland on Saturday, which comes a week after Arsene Wenger's side came from behind to grab a 2-1 victory in the league against those very opponents at the Stadium of Light.
Fellow Londoners Chelsea host Championship Birmingham City on Saturday, knowing defeat would heap further pressure on already under-fire manager Andre Villas-Boas.
Having slipped out of the Premier League top four last weekend with a 2-0 defeat at Everton, Chelsea need to get back to winning ways and keep themselves in with a chance of one major domestic trophy with the league title out of grasp.
Everton, on something of a high after league wins over Manchester City as well as Chelsea in recent weeks, are also in action on Saturday when they host Blackpool, who were relegated from the top flight at the end of last season.
Everton's Merseyside rivals Liverpool will be hoping to get back on the back pages for the right reasons after the storm last weekend over striker Luis Suarez's failure to shake Manchester United defender Patrice Evra's hand.
Kenny Dalglish's side host Championship Brighton & Hove Albion on Su
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.