Fulham boss Roy Hodgson is favourite for the Great Britain job at the 2012 London Olympics.
The Sun says Scotland, Northern Ireland and Wales have all opted out of providing players for the Great Britain squad which will be made up entirely of English players.
That means an English coach is now the obvious choice and Hodgson, 62, is one of the men who has been identified.
FA chairman Lord Triesman said: "I would be very disappointed if we have not appointed a coach for the Olympic team by the end of the calendar year.
"We cannot appoint a Scot, Welshman or Northern Irishman because that would go against our agreement with the other home nations. It would be very desirable to have an English coach."
While Stuart Pearce is also a contender, Triesman insisted the appointment should not be seen as the heir apparent to Fabio Capello.