According to the Daily Mail, talks are at an "advanced stage" between Everton and Tottenham regarding a deal that could see the 33-year-old move to White Hart Lane for a fee in the region of £1.5 million, and on an 18-month contract.
The news comes as a surprise as Neville is highly regarded at Goodison Park and has frequently drawn praise from manager David Moyes for his professionalism and the positive impact he has as captain and a senior member of the squad.
However, Redknapp is believed to be keen to strengthen his options at right-back and few players have handled Tottenham's left-winger Gareth Bale as well as Neville this season.
Redknapp was evasive when questioned about his interest in Neville, though he did not deny Tuesday's reports.
"Phil Neville is a fantastic professional, he is a real leader, a great player, but I'm sure David Moyes knows just how important he is to his team," Redknapp told Sky Sports News. "We played them twice recently and he was a real leader for them, so I'm sure David won't want to lose him, so it will be a difficult one."
If Neville does move to White Hart Lane then he will offer a more defensive option than current right-back Alan Hutton. Croatian Vedran Corluka can also play in the position but has recently been linked with a move away from the club.
Neville could be joined in North London by fellow 1999 Treble-winner Beckham, who is believed to be ready to take a pay cut in order to secure a loan move to Spurs.
Beckham underwent a medical with Tottenham at their training ground on Monday and trained with the club on Tuesday, but talks are still ongoing with LA Galaxy regarding the terms of any loan move. Redknapp is hopeful a deal can be struck.
"It is great to have him here," Redknapp said. "Everyone has worked hard to get him here and we were hoping he would come and play obviously.
"No one could have worked harder than the chairman, Daniel Levy, everybody. They grafted away to try and get a deal done so he could play for us, but it was a bit complicated. You never know, though, and we will see how we go."
Redknapp feels Beckham will be able to hit the ground running if a deal can be reached. He said: "He is a fit lad and looks like he is in great condition. That would not be a problem, but whether it is possible to do it I am not sure."