Liverpool's hopes of finishing in the Premier League's top four effectively ended with a 1-1 draw at Chelsea on Sunday. Liverpool is six points behind United with two games remaining and Louis van Gaal's fourth-place team has a far superior goal difference.
But with Arsenal two points ahead of United with two games in hand, Van Gaal might well have to go through a playoff in August to reach the lucrative Champions League group stage.
Returning United to the European elite was Van Gaal's priority after David Moyes' failure last season following Alex Ferguson's retirement.
Queens Park Rangers, though, is heading into the League Championship. A day after Burnley was relegated, QPR also made an instant return to the second tier after losing 6-0 at Manchester City.
City was playing for the first time since surrendering the Premier League trophy to Chelsea last weekend, with Sergio Aguero scoring a hat trick.
At Stamford Bridge, Liverpool players lined a blue carpet as they welcomed their victorious Chelsea rivals onto the field.
"They deserved a guard of honour but it certainly wasn't nice doing it," Liverpool captain Steven Gerrard said.
Liverpool's defence was equally hospitable in the fifth minute when Chelsea captain John Terry was able to rise to head Cesc Fabregas' corner into the net. It was Terry's 39th Premier League goal — a record for a defender with none coming from penalties— following an 18th assist from Fabregas in his first season at Chelsea.
Gerrard was taunted by Chelsea fans throughout the game over his slip in their game last April which allowed the London club to score and damage its rival's title hopes.
A year later, Gerrard is preparing to end his lifelong association with Liverpool at the end of the month having never won the Premier League.
But the Los Angeles Galaxy-bound player did score his first goal against Chelsea in a decade. Gerrard was left unmarked at the end of the first half to meet Jordan Henderson's free kick with a header.
When the 34-year-old midfielder was substituted in the second half, even the Chelsea fans applauded the player who has only two games remaining in a Liverpool shirt. Given the abuse he has faced since rejecting a move to Chelsea, Gerrard hardly welcomed the gesture.
"I was more happy with the ovation from the Liverpool fans," Gerrard said. "I think Chelsea fans have showed respect for me for a couple of seconds but they have slaughtered me all game. ... It was nice of them to turn up for once today."
It seems unlikely Gerrard will return to the Premier League on a short-term deal after committing his future to Major League Soccer — unlike former Chelsea midfielder Frank Lampard, who signed up Manchester City after being presented by New York City FC last July.
Lampard's spell at City is ending without a trophy but he helped the 2014 champions strengthen its grip on second place with a rout that ended QPR's topflight status.
Aguero took only four minutes to sore by dinking the ball over goalkeeper Rob Green.
Aleksandar Kolarov doubled City's lead directly from a free kick, Aguero netted again at the start of the second half and completed his hat trick from the penalty spot after David Silva was bundled over by Matt Phillips.
After Aguero took his tally for the season to 31 goals, James Milner and Silva compounded QPR's humiliation by scoring.
"Everybody is very disappointed we've lost our status in the Premier League but knew coming here today it was going to be very, very difficult and we would have obviously rather performed better than that," QPR manager Chris Ramsey said. "The club's in a rebuilding phase now."