The former Portsmouth manager insists that there will not be an exodus at White Hart Lane even if Spurs fail to secure qualification for the Champions League this season
Spurs' recent downturn has seen them slide to fifth in the table, having only won one of their last nine league games, and with the possibility that Chelsea may win Europe's top competition, fourth may not even be good enough for Redknapp's stuttering side.
Many of Tottenham's star players are linked with moves away from the club, with Barcelona reportedly in for Gareth Bale and Croatian magician Luka Modric an ever-present in the rumour mill.
But the 65-year-old does not believe they will leave in the summer, whatever comes of Tottenham's Champions League mission.
"When they came to the club, Tottenham weren't in the Champions League, and were nowhere near getting in the Champions League," Redknapp told Sky Sports News.
"They play for Tottenham. They're at a great club. There's no reason they should want to leave. If we don't make it this year, we'll try again next year. There's not too many clubs they could go to better than Tottenham.
"Gareth Bale and Luka Modric have both signed long-term contracts. Gareth has had a fantastic time for a young player at Tottenham. He needs to stay at Tottenham a few more years yet and keep developing."
"We've progressed so much in the last four years, we've got to keep that going and push on even more in the table and look to win a Premier League. It's not impossible."
And Redknapp bade his team follow the example set by Chelsea's senior players last night in the 3-2 aggregate win over Barcelona.
"A club is only as strong as the mentality of its senior players. You look at what Chelsea achieved last night and it is remarkable. It is down to players. When things go well, they take all the credit."
"Great credit to the manager. Robbie [Di Matteo] has done a great job there. He must have a very good chance [of getting a permanent job], a great chance. He's done a fantastic job since he took over."
The former Portsmouth boss highlighted the importance of stringing together an impressive set of closing performances if his Spurs side are to acquire Champions League football next term.
"We've got to make sure we finish fourth or third, make sure we're in a position to qualify," he said.
"If we don't, it doesn't matter what happens. It's still wide open - Arsenal, Chelsea, ourselves, Newcastle - it's still any two from four.
"We've got to go on a good run now."