The 68-year-old, who has also managed West Ham and Portsmouth, is the only man to bring Champions League football to White Hart Lane.
Redknapp, who left Spurs in 2012, made it clear that he thinks his old club is in superb shape to improve in the coming seasons, including the impending campaign.
"I’m a big fan of the manager, Mauricio Pochettino," he told Sky Sports. "I think he’s excellent.
"It’s a great club, they’ve got fantastic facilities, a great training ground, good young players and an outstanding manager in my opinion.
"The futures good. I think Tottenham, with one or two acquisitions in the summer, the right players, they could challenge next year to try and get in the top four.
"They need one or two. I've seen they have some players going to make some room. It’s going to be an exciting Premier League season next season."
What kind of positions do Spurs still need to strengthen in?
The first team players that have the left the club this season, Paulinho and Etienne Capoue, were both signed with the money obtained from Gareth Bale's sale to Real Madrid.
It is unlikely Redknapp means Spurs should add two more central midfielders to directly replace the two outgoings, considering the homegrown players that have come through like Nabil Bentaleb, Ryan Mason, and possibly next season, Tom Carroll. Perhaps one genuinely quality addition would be welcome in this area of the team, but there are so many exciting young midfield talents at White Hart Lane that you could understand Mauricio Pochettino focusing elsewhere.
Other areas of the team like central defence and up front are where Tottenham should look to strengthen, and the 68-year-old may well be impressed if Spurs manage to sign Toby Alderweireld, a defender who starred at another of his old clubs last season on loan.
Otherwise, it is hard to deny that a striker to come in for, or play alongside Harry Kane would also be a smart addition, especially considering the poor form both Roberto Soldado and Emmanuel Adebayor showed last season.