Asked whether the promoted West Londoners were actively pursuing their interest in the former England captain, he replied: "Yes.
"We stuck our hands up. I think David Beckham will obviously look more positively at Spurs than us but let's see in December how we are doing," the Malaysian airline entrepreneur, who also owns Formula One's Team Lotus, said at the Italian Grand Prix.
League rivals Tottenham Hotspur have also said they want to sign Beckham, who trained with Spurs earlier in the year, when his five-year contract with the Los Angeles Galaxy ends in November.
Beckham has made no secret of wanting to play for a united British team as an over-age player in next year's London Olympics and a return to the Premier League would undoubtedly help with that ambition.
Fernandes said that even at 36-years-old, Beckham was exactly the kind of player QPR were looking for.
"If you look at the players we've signed in QPR, they've all got something to prove," the Airasia boss said.
"I told [manager] Neil [Warnock] 'look for players who have something to prove.' Joey Barton's got a lot to prove, especially after his Twitter problem," he added. "Money can't buy that."
Barton, whose former club Newcastle United play at QPR on Monday, is no stranger to controversy and was jailed for assault in 2008. He also criticised the Newcastle board on social media site Twitter before his move.
"Shaun Wright-Phillips, he still feels he can play for England. He needs to play so he's going to get out there. [Armand] Traore, [Arsene] Wenger never really gave him a shot and I think he's a class player," said Fernandes of QPR's other summer signings.
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"Luke Young felt [England boss Fabio] Capello overlooked him. And Anton Ferdinand was lost in the north-east [at Sunderland] and is glad to be back in London.
"So I think David Beckham fits into my profile and of course there are lots of things I could do with him in the other businesses," added Fernandes, whose interests include the music industry.
"Ultimately Neil's the manager and he's got to see if it makes sense and whether David is interested. Let's see. The world is about ideas and exploring things and that's an idea that came up."
Asked how many more players might be signed in the next January transfer window, Fernandes said he would wait and see.
"I don't know. It really depends how [former Blackpool striker] DJ Campbell and [forward Jay] Bothroyd perform. If they perform well, then we've got a great squad."
Fernandes bought QPR from Formula One supremo Bernie Ecclestone and former Renault team boss Flavio Briatore, neither of whom could be considered die-hard supporters of the West London club.
Fernandes said the purchase from Ecclestone had been a "very clean deal."
The new owner twice tried to buy East London club West Ham United, relegated from the Premier League at the en
