The injury-plagued 30-year-old was released by the Barclays Premier League champions at the end of last season and Eriksson was keen to sign him.
However, after being unable to contact Hargreaves, Eriksson told BBC Radio Leicester: "It will not happen now. If it was going to happen it would have already been done, but now it is too late.
"I can't reach him. I have only spoken to his agent and he has not come back to me, which is a little bit strange."