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.
Blackburn sit 13th after a patchy start to the season and will be keen to respond to a 3-2 home loss to Derby County on Wednesday.
Derby next welcome Cardiff, who also sacked their manager - Ole Gunnar Solskjaer - on Thursday.
The former Manchester United forward arrived in south Wales to much fanfare after guiding Molde to two titles in Norway but his failure to keep them in the Premier League has been followed by a disappointing Championship start.
Tuesday's 1-0 home loss to Middlesbrough left them 17th in the table with just eight points from seven matches.
Danny Gabbidon and Scott Young will take charge for their visit to Pride Park to face a Derby side who are unbeaten in four.
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.
League leaders Forest are one of just two sides still unbeaten this term and they travel to a Millwall side who have faded after a bright start, losing three of their last four.
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.