Redknapp last week believed Defoe to be subject of a "massive offer" from elsewhere, but on Wednesday he suggested a deal could still be struck with Pompey boss Tony Adams and chief executive Peter Storrie.
Defoe is one player on what Redknapp describes as a "very short list" of January transfer targets, with the Spurs boss prepared to miss out if prices are inflated.
Of the Defoe deal, Redknapp said: "If the price is right and if Tony and Peter Storrie want to sell him and it's what we consider at our valuation and theirs, then fine.
"There are other options as well, I have a little list and if we don't get one we can move to another. If we can't get them then we won't be getting anyone."
A striker, a left-sided midfielder and a reserve goalkeeper to cover for Heurelho Gomes are Redknapp's priorities.
He said: "I don't think we'll be splashing vast amounts, the chairman asked who I'd want if we could get them. If we can end up with a couple then great.
"You get agents calling up offering players and it would only cost you your job if you took them.
Tottenham Hotspur boss Harry Redknapp admits a return to White Hart Lane for Jermain Defoe is a possibility if a fee can be agreed with Portsmouth.
"I know exactly what I want and it is a waste of time calling up for anyone else. I have a very short list of players that interest me and if we can get them then great."
Redknapp does not predict a huge amount of spending when the window opens next month, although he feels Manchester City's wealth will play a crucial role.
"Everyone thinks Man City are going to come in and pay way over the odds for everybody because of the money they've got, but I don't think they will," he said.
"Mark Hughes is a very clever manager, he might want the players but I don't think he'll sit back and let the owners pay vastly inflated fees for players he does not feel are worth that kind of money.
"I think that is the key, if a chairman hears Man City might be interested in one of their players they could say, 'Let's hang on and we could double our money'. I don't think that will happen, Mark is too shrewd for that."