Fernandes claims the former England captain's advisors are interested in discussing his vision for Rangers, and says the 36-year old, like new signings such as Joey Barton and Shaun Wright-Phillips, has something to prove in the Premier League.
"Environment, love, care and attention - we can offer that to him," Fernandes told reporters in Monza ahead of the Italian Grand Prix.
"They [Beckham's advisors] want to talk because our vision is a long-term one, with lots of things David can do in Asia with me. It's something we have to work at.
"If you look at the five signings we've made we have brought in people who have something to prove.
"Shaun Wright-Phillips still feels he can play for England; Joey Barton has a lot to prove; Anton Ferdinand, missing in action at Sunderland, but back in London, home town, things to prove.
"Then we've Luke Young who felt he was deserted early by [England manager Fabio] Capello, and [Armand] Traore was never given a chance at Arsenal by [manager Arsene] Wenger.
"So we've five new players, and Beckham fits into that mould because he wants to return and captain Britain at the Olympics."
Fernandes maintained, however, that any such deal remained only an "idea" and that he would seek the approval of manager Neil Warnock beforehand.
"I'm not sure it's for him, and I'm not sure it will fit him in January," Fernandes admitted. "Who knows?
"But I'm an ideas man, and he is an idea. He may not want it, he may want a bigger club. I hear [Tottenham Hotspur manager] Harry Redknapp has said he wants him.
"Ultimately, Neil has to feel comfortable, but who knows what can happen in January. We will have to wait and see."
The Malaysian-born tycoon also elaborated on his plans to balance his time between QPR and his Formula 1 team, Team Lotus.
"Football is huge in my part of the world, much larger than in F1, which of course is a huge global sport," he said.
"I have looked at each business and the resources required, and whether we can do it.
"And a football team and a Formula One team have many ways of collaborating and increasing the pie for each other, so I feel comfortable."