Redknapp has always been an admirer of the energetic former Manchester United man, who has the ability and temperament to play down the left side or through the middle.
It is as an attacking midfielder that he has scored four goals in his last three outings for Sunderland, which has coincided with Spurs' renewed interest a player they courted 20 months ago.
With the future of Gareth Bale far from certain at White Hart Lane, Redknapp has to consider a number of candidates to come in should the Welshman leave.
Inter Milan are thought to be readying a £40m close-season offer for Bale and, although Tottenham would prefer to keep him, last month's hectic transfer window highlighted that every player has his price.
Tottenham's main summer target is likely to be Blackpool's Charlie Adam.
Aston Villa's Stewart Downing and Manchester City's Adam Johnson could also be in the former Portsmouth boss' mind, Richardson's versatility could prove crucial.
Redknapp remains on the look out for a new left-back, with Benoit Assou-Ekotto and Bale, who he prefers to play further forward, are his only natural options.
Sunderland manager Steve Bruce has used Richardson, who prefers to play further forward, regularly on the left side of the defence.
The 26-year-old, who cost £5.
5m when he moved from United in 2007, only signed a new three-year deal last summer and that would strengthen Sunderland's hand in any negotiations, while it could also help them if they decided to pursue any of Tottenham's strikers.
Bruce's priority this summer remains to bring in a new striker following the January departure of Darren Bent and is unlikely to go back in for Stoke City's Riccardo Fuller.
Tottenham remain in touch with the top four in the hope of finishing in a Champions League berth for the second season in a row - and they will look to further improve that when they travel to Wearside tomorrow.
Sunderland defender Nedum Onuoha, who outlined this week that he would like to stay at the Stadium of Light, is expecting a rough ride from Bale et al - if the Spurs wing-wonder recovers from a back problem.
"It's usually quite intense when you play against Bale, and they've also signed (Steven) Pienaar and you've got Niko Kranjcar, they can all play on that side," said Onuoha, on loan from Manchester City.
"So whichever way you look at it, it's tough.
Bale didn't play last Saturday but I'm sure he'll be available.
You can see why they're having such a good season, and I fancy them to beat AC Milan in the Champions League.
"That speaks for itself, in terms of how far they've come on over the past few years.
If you'd said that a few years ago you'd be called crazy.
" Sunderland face Spurs needing to show strength of character having failed to stand up to the aerial bombardment dished out by Stoke City last weekend.
Despite looking like returning to the North-East with a positive result, Stoke's direct style earned them three points in the end and that led to Liverpool leapfrogging them in sixth place ion the Premier League.
Onuoha said: "It makes myself and the other players more determined.
There's nothing worse than when you lose a game.
You just want to get to the next game and win that.
"You can never really feel sorry for yourselves because that's going to get you in to a situation where you lose every single week.
"I don't think we've ever had that this season, I think the most number of games we've lost on the bounce is two, and we've come back with a win after that.
"I think we could finish very high this season but there are a lot of very difficult games coming up in the next month and a half.
Then after that we've got games we could win, based on our league position.
"You never know where you might finish but at the end of the day it's going to be down to ourselves and hopefully we won't have to rely on any favours to finish as high in the league as possible.