Veteran manager Ottmar Hitzfeld is understood to have held informal talks with Fulham over the vacant manager's job at Craven Cottage.
The 62-year-old German has two years left to run as manager of Switzerland, whom he guided to a shock 1-0 victory over the eventual world champions Spain during the group stages of the World Cup.
Hitzfeld is thought to have indicated he would be keen to move to Fulham, who have also approached the former England manager Sven Goran Eriksson about the possibility of replacing Roy Hodgson, who left last month to take charge at Liverpool.
The German is one of the most highly respected managers in the world, having twice been voted world coach of the year. A former maths teacher, he has won the European Cup twice, leading Borussia Dortmund to a 3-1 victory over Juventus in 1997 before guiding Bayern Munich to glory on penalties against Valencia in 2001.
Nicknamed "The General", he is Germany's most successful manager of all time, with 13 major trophies plus five more with clubs in Switzerland.
Bob Bradley, the coach who led the United States to the knockout stages of the World Cup, is also understood to be on the club's shortlist.
The 52-year-old American has just five months to run on his deal with the national team. He currently earns £330,000 per year but would expect to receive around £1m at Fulham.
Fulham's owner, Mohamed al-Fayed, wants a manager with proven international experience to replace Hodgson to ensure the club do not regress next season following this year's achievement in reaching the Europa League final. Other candidates include Ajax manager Martin Jol, Stuart Baxter, the coach of Finland, Slaven Bilic, Mark Hughes, Alan Curbishley and David Jones.