Redknapp has been linked with a host of possible targets in the last week as he bids to save QPR from relegation and Cole, who made his senior debut at West Ham under Redknapp, has been tipped to move back to London after failing to make an impact on Merseyside.
Speaking about the 31-year-old, Redknapp said: "I like Joe, I had him as an 11-year-old. The talent is there and I think there's still a top player in there. I haven't made any enquiries yet - I haven't made any enquiries for anyone."
The former Tottenham manager also played down talk of a January move for Marseille striker Loic Remy, who was heavily linked with Spurs during Redknapp's spell at White Hart Lane.
He added: "I was interested in Remy but that was then. It's a different situation now. He would be expensive. It depends on where we are in January.
"I've never discussed players with anyone. Here we are, we need to win matches now. January is way off."