Eriksson revealed earlier this month he had failed in an audacious attempt to sign the LA Galaxy midfielder, who was England skipper during the Swede's reign. Beckham revealed on Sunday night, after receiving the BBC Sports Personality's Lifetime Achievement award, that he plans to play in Europe this winter in a bid to win back his place in the England squad.
Eriksson admits it is unlikely Beckham will agree a move to the Walker Stadium, but the Foxes boss will make one more attempt to pull off what would be a stunning signing.
Eriksson told BBC Radio Leicester: "I would try again and that would be the third time.
"But no, he will not come - I am pretty sure - so we can forget that story."