The former Three Lions boss has been open about his desire to bring Beckham back to England and has revealed that the LA Galaxy star hasn't ruled out the move.
"I have already had that discussion with him," Sky Sports News quotes Eriksson as saying.
"I spoke to him about Leicester. Beckham, he will never say no to me - he says, 'Sven, we'll see, we'll see'.
"The big thing is what he wants to do when his contract finishes in LA. Will he want to go on playing? If he wants to play, I will try again."
"I guess most of the clubs in England will take him, as a good football player and for the image," Eriksson added.
"We will do it at once, of course. We will give him a whistle and he can go out [on the training pitch] straight away."
Meanwhile, Beckham has hailed Robbie Keane since his arrival to the Los Angeles MLS club in August.