QPR and manager part company and United draw Liverpool.
Draw with Dons the last straw for Neil Warnock
Rangers lie 17th in the Premier League table, having won just five of their 20 top-flight games this.
Warnock, who led them to the Championship title last season, has now been removed from the post, with former Fulham boss Mark Hughes strongly linked with the new vacancy at Loftus Road.
In a statement, QPR chairman Tony Fernandes, said: "This decision has been made in the best interests of the club and I can assure everyone that this is not a decision that was made lightly."
The club statement said on qpr.co.uk: "Queens Park Rangers Football Club has today parted company with Manager Neil Warnock.
"Last season, he successfully guided the club back to the Premier League for the first time in 15 years.
"The board's commitment to retaining our Premier League status ultimately led to this decision. Fernandes, who took over the club in the summer, added: "Sadly, our recent run of poor form has seen us slip alarmingly down the table and the board felt it was the right time to make a change."
QPR will face Chelsea if they can see off MK Dons in their replay.
United, who overcame City 3-2 at the Etihad Stadium, will face the Reds on the weekend of January 28 and 29.
The game will be the first meeting of the two sides since the controversial clash in October when Liverpool forward Luis Suarez racially abused United defender Patrice Evra.
Chelsea captain John Terry could make a first return to the ground since he was accused of racially abusing Rangers defender Anton Ferdinand, a matter which has become the subject of a criminal case and an accusation which he strenuously denies.
Arsenal will be at home to Aston Villa if they can overcome Leeds at the Emirates Stadium Monday night, while Bolton will take on Swansea at the Reebok Stadium if they see off Macclesfield in a replay. Tottenham Hotspur travel to Watford.