Fulham had been left red faced earlier this week after their failure to land Ajax coach Martin Jol, but Al Fayed will not be rushed into appointing a new dug-out chief.
Klinsmann, hailed as the man who masterminded and matured Germany's latest national team, has been out of work since leaving his post as Bayern Munich manager last summer.
The former German international is currently living in California and is not believed to have applied for any jobs.
However, it is reported that the former Tottenham Hotspur striker would jump at the chance of a return to the Premier League.
Fulham are prepared to offer their new manager a £20m transfer war-chest and a wage in excess of £2m a year.
Current caretaker boss, and Fulham stalwart, Ray Lewington is overseeing pre-season preparations with the Cottagers on a tour of Sweden.
Yet it has been speculated that several first-team players are keen for a new manager to be installed as soon as possible so that their future at the club can be assured.