Livermore broke into the Spurs first team under Redknapp, but his game time has been significantly more limited under new boss Andre Villas-Boas.
"Yeah, we're taking Livermore," Redknapp told reporters.
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But Tottenham's Portuguese boss was less committal on Livermore's potential loan move, stating that the deal was yet to be concluded.
"There’s nothing confirmed yet," Villas-Boas said after watching his side draw 0-0 against QPR. "I think when we announce it, it will be official from all three parties."
Redknapp – currently short of quality strikers in his squad – also confirmed his interest in bringing West Brom's Nigerian forward Odemwingie to Loftus Road, a player he has long admired.
"We made an enquiry for Odemwingie, yes," the QPR boss revealed.
"I don't know whether [chief executive] Philip Beard has put an offer in, but he was a player that we spoke about and he’s someone that I was interested in making an offer for.
"And there's every chance we have made an offer for him, but I haven't spoke to him [Beard] today. Probably an offer may well have gone in.
"I don't know what’s happened with the offer, if there is one. He's just a player that I spoke about, I said he was an interesting player, find out if West Brom would sell him and that's how I left it with the chief executive to try to find out for me."