At his first press conference since taking over at Loftus Road, Redknapp told reporters that Beckham had sent him a text wishing him luck in the Rs' hot seat but denied ever discussing a move for the 37-year-old with chairman Tony Fernandes.
The ex-Tottenham manager was keen to concentrate on the players already on the books of the struggling side but admitted that he still regarded Beckham as a valuable asset for any club.
"I got a lovely text from David the other night, not talking about himself coming but just wishing me all the best here," Redknapp told reporters. "He's a top professional but I've never discussed the possibility of him coming.
"I think at any football club he'd be a great influence but I've not discussed anything. I've not discussed [new] players at all with the chairman at the moment. There's loads of ability here, we've got to get the best out of this group now. What happens in January is way off."
Redknapp refused to be drawn on speculation linking QPR with a renewed attempt to sign Tottenham defender Michael Dawson in the January transfer window after the club chased the centre-back's signature during the summer.
"Michael's a top player again," Redknapp commented. "The transfer window and transfer speculation is nothing, it's not on my mind at all.
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"I'm only thinking about the group I've got here. Buying players, loaning players is a long way away. If we don't pick some points up, what's the point?"
The 65-year-old insisted that Adel Taarabt would remain a key contributor for the Premier League's bottom side despite his decision to sell the Moroccan when in charge of Spurs.
"I sold him, but he wasn't a player I wanted to sell," he claimed. "I thought he had great ability. He couldn't get in the team at Tottenham, it was difficult. He had [Luka] Modric and [Gareth] Bale and God knows who keeping him out of the team.
"It was difficult for Adel but I always felt he had the ability to become a top player. I've got to get the best out of him and if we can do that, he's a match-winner."
Redknapp would not comment on the future of midfielder Joey Barton, meanwhile, with the former QPR captain spending the current season on loan at Marseille.
"He's on loan for the season, he's not here, so he's not going to help me [in the short-term]," he stated. "I'm not thinking about next season. We're in the present, the future is down the line. We need to get cracking right now."