Redknapp is keen to bolster his squad with three further signings ahead of the transfer deadline and has been linked with Aston Villa duo Milner and Young.
Milner is set to speak with Villa about his future after being identified as a possible target by big-spending Manchester City.
If a switch to Eastlands does not go ahead, speculation has suggested that Spurs may try to snap him up.
Milner's team-mate Young has also been connected with a move to White Hart Lane, with Villa boss Martin O'Neill admitting that he does expect interest in the winger.
Redknapp admires both Milner and Young but says he has not approached Villa about either player and has no intention of doing so.
Asked about Milner, Redknapp told Sky Sports News: "No, we wouldn't be able to.
"Anybody would like James Milner, he's an outstanding young player, but he'd be way out of our depth."
On Young, Redknapp added: "Again, I wouldn't think they'd want to sell Ashley Young.
"He is a good player but he belongs to Villa. We've not made any enquiries for him at all."
Redknapp is considering a defensive swoop with Jonathan Woodgate certain to miss the start of the season and Ledley King also struggling with his fitness.
However, he has ruled out a move for Everton's Jagielka and still believes there is a chance that King could be ready for the big kick-off.
Questioned on whether he would be targeting a new centre-back, Redknapp stated: "It's a possibility.
"I am hoping Ledley might be OK. His knee is swollen at the moment but it goes down so we will have to wait and see."
Asked specifically about Jagielka, the Spurs manager continued: "A good player again, outstanding player, but we wouldn't be in the market for someone like that."
Redknapp remains in the market for a third goalkeeper and hopes to push through a loan deal for Croatian Stipe Pletikosa.
"I think Daniel (chairman Daniel Levy) is talking to him and there is a possibility of loaning him," Redknapp revealed.
"We have two outstanding goalkeepers in (Heurelho) Gomes and Carlo Cudicini but I do feel that maybe we need three keepers with European games coming up. It is something we are interested in doing."