Former England Under-21 international Routledge is in talks with the Foxes after Newcastle accepted a ?1.5 million bid for their sought-after winger.
Routledge has been the subject of interest from a host of clubs this summer, including Premier League new boys QPR after he spent the second half of last season on loan at Loftus Road.
Ninth club: Wayne Routledge is set to leave Newcastle for Leicester
Another newly-promoted club, Swansea City, were also keen on the 26-year-old winger, while he has been linked with Championship trio Birmingham, Cardiff and Nottingham Forest.
But Leicester, who have been busy reinforcing their squad over the past couple of months in preparation for the promotion challenge demanded by their Thai owners, are confident of clinching a deal.
Farewell: Routledge has just completed a second spell at QPR
Eriksson has already signed ex-England striker David Nugent and splashed a club record ?5.5 million to capture central defender Matt Mills from Reading.
He has also signed goalkeeper Kasper Schmeichel, Lee Peltier, Neil Danns and Republic of Ireland international defender Sean St Ledger.
CLICK HERE TO SIGN UP FOR OUR FREE FANTASY FOOTBALL GAMESwansea make ?1.5m bid for out-of-favour Newcastle winger RoutledgeAll the latest Newcastle United news, features and opinion