Rooney's Rams face a replay at home to the League Two side after a goalless draw on Friday night, while League One Shrewsbury will face Chelsea if they can see off Premier League leaders Liverpool at Anfield.
Here, the PA news agency takes a look at the headline ties from Monday's draw.
Northampton or Derby v Manchester United
Northampton, the lowest-ranked team left in the competition, face a stiff task to see off Championship Derby in a fourth-round replay. But the reward will be a home tie with Manchester United.
The Cobblers famously hosted United at the County Ground 50 years ago, when United won 8-2 and George Best scored six goals on his comeback from a four-week ban for kicking the ball out of a referee's hands. Two visits by United this century in cup competitions both ended in away victories, too.
But standing in Northampton's way of another dream tie is United's all-time record goalscorer Rooney and his Rams team-mates who will be looking to make amends for Friday's goalless draw and get another crack at United.
Their last encounter with the Red Devils saw Derby win 8-7 in a penalty shoot-out at Old Trafford in the EFL Cup in September 2018.
Chelsea v Shrewsbury or Liverpool
Shrewsbury's FA Cup run looked to be drawing to a close when they found themselves 2-0 down at the Montgomery Waters Stadium to a Liverpool side comprised largely of young players seconds after half-time.
But substitute Jason Cummings' second-half double cancelled out Curtis Jones' strike and a Donald Love own goal to set up a trip to Anfield in which Reds boss Jurgen Klopp has already indicated he will field a youth team during the Premier League's first winter break.
Eight-times winners Chelsea booked their place in the fifth round with a 2-1 win at Hull, although they had to survive a concerted fightback as substitute Kamil Grosicki halved their lead following goals from Michy Batshuayi and Fikayo Tomori.
Sheffield Wednesday v Manchester City
Having put out top-flight Brighton in the third round, Sheffield Wednesday made it to the last 16 courtesy of a 2-1 victory in their all Sky Bet Championship tie at QPR.
Goals from Morgan Fox and Sam Winnall were enough to see the Owls through despite Nahki Wells' stoppage-time effort as Garry Monk's men bounced back from a 5-0 drubbing by Blackburn on their own pitch the previous weekend.
Their reward is a home clash with holders and Premier League giants Manchester City, whose defence continued with a 4-0 win over Championship Fulham thanks to a Gabriel Jesus double, Ilkay Gundogan's penalty and Bernardo Silva's strike.
The sides met at the Etihad Stadium in the Capital One Cup in September 2014, when City romped to a 7-0 victory, but they needed two second-half goals from James Milner to progress in the FA Cup when they last locked horns three and a half months later.