Spurs had expressed interest in the 34-year-old Toffees captain but have been told by Everton boss David Moyes that the player is not for sale.
"That's the only one," Redknapp replied when asked by Sky Sports News if there could be a late move for Neville. "We've made an offer to Everton. It's up to Everton. If David doesn't want to sell him, that's fine.
"That's the only one - if anything was going to happen that's a possibility but I doubt very much whether there'll be any business from us at all."
Reports linked Tottenham with a move for a host of strikers, with suggestions the club had turned their attention to Diego Forlan after missing out on his Atletico Madrid team-mate Sergio Aguero.
It was rumoured that Spurs had tabled a £17 million bid for the 31-year-old former Manchester United man, who has also been linked with a move to Real Madrid.
Asked if a new striker would be arriving, Redknapp said: "Definitely not. There's nothing happening at all there. I don't know where the stories were coming from. All these people were suddenly linked with us."
Forlan arguably has unfinished business in England having flopped during his two-year stay at Manchester United.
The day started with reports that Spurs had tabled a club-record £38.5 million bid for Forlan's team-mate Aguero, who has also been linked with a move to Real Madrid and Chelsea.
The Argentina striker put an end to speculation about his future by signing a new contract with the club he joined five years ago. The 22-year-old agreed a two-and-a-half-year extension to his existing deal earlier this month and formally signed the contract at a presentation in Madrid on Monday afternoon.
The new deal reduces the buy-out clause in the player's contract but Aguero himself insisted that he never thought about leaving Atletico.
Aguero said: "If I wanted to leave the club I wouldn't have signed a new contract. I have always said that I will decide when I want to leave, neither the club nor my agent will decide. I'm happy here. Ever since I arrived at this club as a 17-year-old I have always felt like it was my home and the club has treated me well."
Spurs were also linked with several other strikers in Spain. Villarreal star Giuseppe Rossi, Athletic Bilbao's Fernando Llorente and Sevilla hitman Alvaro Negredo were all said to be on Redknapp's radar but the Spurs boss was pessimistic about his club's chances of signing any of them this morning when he pulled up to training.
"Rossi is a fantastic player but I wouldn't have thought so. Negredo is a top player. Llorente? We'd have all of them. They would improve us but I can't see any of them being here," Redknapp added.
Redknapp allowed Robbie Keane to join West Ham, while Giovani dos Santos has gone on loan to Racing Santander.
Tottenham are facing a major crisis in defence after Michael Dawson's red card at Fulham yesterday which means he will miss the next three games.
With fellow centre-half William Gallas struggling with a hip problem, Redknapp admits that he may now have to turn to Jonathan Woodgate, who has been out for over a year with a serious groin problem and was originally supposed to go out on loan to aid his recovery.
"Jonathan Woodgate is going to be pushed into action quicker than expected," Redknapp added. "We'll have to see how Jonathan is. Hopefully he has had no reaction from his injury and we hope that he could be available pretty quickly for us now."
Meanwhile, Everton have confirmed the signing of Greek teenager Apostolos Vellios. The 19-year-old striker has joined from Greek side Iraklis Thessaloniki for a nominal fee.
Vellios, who has scored seven goals in 14 appearances for the Greece Under-19 team, has penned an agreement until 2014. The Toffees have also confirmed two squad players will be leaving the club on loan until the end of the season.
Joao Silva, 20, has joined Portuguese first division side Uniao de Leiria while 21-year-old Kieran Agard has secured a move to Scottish outfit Kilmarnock.