QPR and Tottenham, with whom he trained last winter, have been touted as possible destinations, but Leicester boss Eriksson is hoping to link up once again with the man who captained England during his tenure as manager.
Eriksson told The Times: "I have already had that discussion with him. 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?"
Eriksson knows the npower Championship side, who have received substantial investment from their Thai owners, will face stiff competition from other clubs in England, while Paris St Germain are also reported to be interested.
However, the Swede hopes the added incentive of a training role will help tip the balance.
"We will give him a whistle and he can go out (on the training pitch) straight away," he said.