Liverpool forward Keane has been linked with a return to White Hart Lane after only appearing in half of the Reds last 12 games and sensationally being left out of the 18-man squad which faced Everton in the FA Cup on Sunday. Redknapp earlier said he would like a player of Keane's quality, but when asked after Tuesday's 3-1 win whether he thought he could lure the Irishman back he replied "I wouldn't of thought so."
The former West Ham boss was also pessimistic about the capture of Lyon forward Fred after the Brazilian was heavily linked with a move to Spurs. The 25-year-old is out of contract at the end of the season and has indicated his desire to leave the French champions.
"If I could find a very good centre-forward then I'd get one," the ex-Portsmouth manager said. "He (Fred) was meant to come today but didn't turn up so don't bet on him coming tomorrow. He's out of contract in the summer and I think they want a small fee for him."
Club-less Ghana captain Stephen Appiah has been training with the north London side this month and Redknapp says he will make a decision about the 28-year-old's future on Wednesday.
Redknapp should have few relegation worries while Luka Modric is in such good form. Tottenham's convincing win against Stoke was inspired by the Croatia midfielder. Former Dinamo Zagreb star Modric helping to set up goals for Michael Dawson and Jermain Defoe, with winger Aaron Lennon grabbing the other.
Redknapp was full of praise for the slight playmaker. He said: "Modric was absolutely fantastic and ran the game. He's not only a great footballer but he has a massive heart. The first time I saw him I thought he was like Eyal Berkovic who I had at West Ham. He was a fantastic player with the ball but not so good without it, but this guy's different altogether."
Redknapp said he would consider changing his winning team to accommodate new £14 million signing Wilson Palacios. "I've got to try and balance the team right and I need to get Palacios in there because he's everything I want in a midfield player," he added. "Between Zakora, Palacios, Modric and Jenas I'm strong in midfield but I can't play Defoe on his own up-front."
Lennon was revealed to be carrying a groin injury so it is likely he will be the one to make way for Palacios, but the manager has some selection headaches when his squad is back to full strength.