Recent reports suggested that the Hoops were considering lining up a three-month loan deal to bring the Republic of Ireland striker to Loftus Road.
Keane hit the matchwinner for LA Galaxy against New England Revolution to clinch a fifth MLS Cup.
But Redknapp was quick to dismiss suggestions that QPR have made a bid.
"There's been no approach. Robbie [Keane] has been a fantastic player.
"He's gone over to the USA and he hasn't gone for a holiday. He's been an amazing footballer.
GETTY
Harry Redknapp insists QPR haven't made an approach for Robbie Keane
He belongs to LA Galaxy but there have been no enquiries
Harry Redknapp
"He belongs to LA Galaxy but there have been no enquiries.
"The first I have heard of it was when I read it in the papers on Monday."
Jermain Defoe has been another striker linked with a move to the Premier League strugglers, but once again, Redknapp downplayed suggestions a deal was on the horizon.
He added: "I've not spoken to Jermain [Defoe]. We tried to strike a deal in the summer, but he was too expensive."
Redknapp hinted that QPR may look to sign two players in the January transfer window, but said he would only bring in reinforcements 'if necessary'.
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