Both clubs were relegated from the Premier League last term and have not adjusted well to life in the second tier, with Fulham propping up the division after Wednesday's 5-3 loss at Nottingham Forest.
That result proved the final straw for Fulham owner Shahid Khan, who sacked German coach Felix Magath a day later.
Fulham smashed a Championship record when parting with £11million to lure Ross McCormack - the division's top scorer last term - from Leeds United.
But their performances have been dreadful this season, picking up just one point in seven matches, with Kit Symons handed caretaker duties ahead of Saturday's home clash against Blackburn Rovers.
Derby next welcome Cardiff, who also sacked their manager - Ole Gunnar Solskjaer - on Thursday.
Tuesday's 1-0 home loss to Middlesbrough left them 17th in the table with just eight points from seven matches.
Steve McClaren's side lost the play-off final last term but appear well-placed for another promotion tilt after holding on to the likes of Craig Bryson, Will Hughes and Chris Martin in the transfer window.
Leeds are also without a manager but enter Saturday's Yorkshire derby against Huddersfield Town at Elland Road in good spirits.
Leeds are unbeaten in three matches under caretaker Neil Redfearn, winning two, and Tuesday's 3-1 come-from-behind win at Bournemouth lifted them to 14th in the table. They also won the corresponding fixture 5-1 last season.
Hot on Forest's heels are Norwich City and a home clash against Birmingham City will give them every chance of keeping the pressure on Stuart Pearce's men.
The other unbeaten side, Charlton Athletic, travel north to face Rotherham United while third-placed Watford host Bournemouth.
Other sides in the play-off places - Wolves and Reading - face Bolton Wanderers and Sheffield Wednesday respectively.
Blackpool's search for their first win takes them to Brighton and Hove Albion, while Middlesbrough meet Brentford. In Monday's only fixture, Wigan Athletic host Ipswich Town.
