The Blues slumped to a surprise 2-1 home loss against Swiss club Basle in the Champions League on Wednesday evening, which was a second straight defeat after the Barclays Premier League reverse at Everton.
Mourinho has never lost a Premier League home game, winning 48 and drawing 14, an impressive record which stretches back through his first spell in charge.
Fulham, though, having drawn five of the last seven meetings against their SW6 neighbours, which included a narrow penalty shoot-out defeat at Stamford Bridge in their 2011/2012 Carling Cup tie.
Norway defender Hangeland sees no reason why his team-mates cannot get another positive result if they approach the Saturday 5:30pm kick-off in the right frame of mind.
Speaking to the club's official website, www.fulhamfc.com, he said: "We will just focus on ourselves, make sure we are well prepared and ready to go. If we do that, it is always possible to get a result.
"It is definitely not an easy place to go to, because they have a fantastic team with world-class players.
"But as I said, they tend to be tight games and we've done quite well there over the last few seasons, picking up some draws, so anything is possible."
Like Mourinho, Fulham boss Martin Jol is not having it all his own way this season either, the Dutch coach apologising for his public outburst against those supporters who booed the 1-1 draw with West Brom last weekend, where the home side conceded a costly equaliser in stoppage-time.
While Jol accepts it will be a stern challenge to take all three points the mile or so back down Fulham Road to the banks of the Thames, he believes the squad can take confidence from recent performances against the Blues.
''I have to put it in the minds of my players that we had good results (there),'' the Fulham manager said.
''I don't know what that means to have good results in the away matches against them, but we still know the way we played against them, so maybe that will help."
Striker Dimitar Berbatov will have a fitness test on a hamstring problem, and Bryan Ruiz (ankle) misses out, but forward Darren Bent should be back in the squad following his own hamstring issues which forced him to miss the 1-1 draw with West Brom.
Fulham chairman Shahid Khan, meanwhile, believes removing the controversial Michael Jackson statue outside Craven Cottage is the ''right thing'' to do.
Former owner Mohamed Al Fayed, a close friend of the late performer, commissioned the sculpture which was erected outside the west London stadium in April 2011, but it is now set to be returned to the flamboyant Egyptian-born entrepreneur as Fulham press on with the redevelopment of the Riverside Stand.
''Our supporters' views on the statue have been made clear,'' said American-based Khan, who completed his £150million buy-out earlier in the summer.
''I respect Mr Al Fayed and know he had good intentions in paying an individual tribute. However, the removal of the statue is the right thing for Fulham Football Club.''