Although the Huddersfield Town boss was linked with the job last week, it seems the London club have bigger fish to fry.
The new manager will be named shortly before the players fly to Sweden for a training camp on July 19.
It has emerged that while Sven-Goran Eriksson remains the most likely man to replace Hodgson, however a new contender has emerged: Slaven Bilic, the former West Ham and Everton player.
Glenn Hoddle, Mark Hughes, Tony Mowbray, Alan Curbishley and Gianfranco Zola are believed to be out of the running.
Ray Lewington, the caretaker since the departure of Hodgson to Liverpool, will take charge in the friendly against Brentford, at Griffin Park next Wednesday.