The defender, 24, has not kicked a ball competitively in eight months after suffering a series of injury setbacks.
Chalobah was the subject of interest from Bayern Munich last summer, with boss Thomas Tuchel handing the ace his debut in 2021.
He has since played 63 times for his boyhood club, scoring three goals in the process.
But Chalobah is now said to be firmly out of Mauricio Pochettino’s plans.
Chelsea owner Todd Boehly is eager to cash in on the club’s academy-grown players, with Conor Gallagher and Armando Broja also up for sale.
And Chalobah is expected to depart Stamford Bridge before the end of the month.
A move to Bayern looks unlikely after the Germans pounced for Tottenham misfit Eric Dier.
But Sky Germany claims Fulham are now ready to make an approach, just days after losing to Chelsea in the west London derby.
Marco Silva is said to be a big fan of Chalobah’s versatility, with the centre-back also capable of play as a right-back and defensive midfielder.
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Fulham are now set to open talks with Chelsea over a six-month loan deal.
And they would also like the option to make his move permanent in the summer.
However, West Ham are also tracking Chalobah.
And they are able to offer him Europa League football after cruising through the group stage.
SunSport exclusively revealed at the start of January that Tottenham were keeping an eye on Chalobah.
But their interest looks to have ended after they saw off Bayern to land Radu Dragusin from Genoa.
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