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.
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.
"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."
"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.
"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."
"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 said the purchase from Ecclestone had been a "very clean deal."
