The Red Devils sit 22 points adrift of Premier League leaders Manchester City after a 1-0 defeat to Wolves in their previous fixture, while a 2-1 loss to Brentford made it back-to-back defeats for Villa for the first time under Gerrard's tenure.
A decent FA Cup run would not be sniffed at by either manager.
Recent form for Manchester United and Aston Villa
United's loss to Wolves was Rangnick first as interim manager but it wasn't completely out of the blue with United having failed to inspire in their draw against Newcastle and narrow win over Norwich.
Nevertheless, United were eight games unbeaten in all competitions before the reverse, a run fuelled by the departure of Ole Gunnar Solskjaer as head coach.
Danny Ings' first goal since October proved in vain against Brentford. But having taken over with the Villans fearing a relegation scrap, Gerrard's arrival has instilled a real feelgood factor around Villa Park, a mood enhanced by the acquisition of Brazilian Philippe Coutinho.
Manchester Utd 0-1 Aston Villa (September 25, 2021)
Aston Villa beat Manchester United for the first time since December 2009 when the two teams met in the Premier League earlier this season.
A late header from Kortney Hause stunned the 72,000 at Old Trafford, although the drama did not end there. Hause was deemed to have handled the ball by referee Mike Dean who awarded the Red Devils a late penalty that was hammered over the bar by Bruno Fernandes.
Steven Gerrard will be hoping for a better outing against Manchester United than his last appearance as a player, which saw him sent off 38 seconds after coming on as a substitute in March 2015.
Past 10 meetings
Manchester Utd wins: 7
Aston Villa wins: 1
Manchester Utd goals: 20
Aston Villa goals: 8
Previous FA Cup runs
Aston Villa have not had much luck in the FA Cup in recent years and have to go back to 2016 for their last victory in the competition.
A 2-0 replay victory over Wycombe saw them progress to the fourth round where they were hammered by Manchester City.
Manchester United have enjoyed much better fortunes in the FA Cup and the last time they failed to make it to at least the quarter-finals was in 2014.
However, since lifting the trophy in 2016 under Louis van Gaal, the Red Devils have only reached the final once, finishing runners-up to Chelsea in 2018.
The visit of Villa is only the second time in ten years that United have faced Premier League opposition in the third round.
Team news/predicted line-ups for Man Utd vs Aston Villa
Ralf Rangnick seems intent on fielding a strong team in the FA Cup despite calling for the League Cup to be scrapped only last month after concerns with fixture congestion.
With an injury concern for Harry Maguire and Eric Bailly away at the Africa Cup of Nations, Sweden's Victor Lindelof may be required in the starting XI after some time out with Covid-19. Phil Jones will also hope for a second consecutive start after a much-vaunted display against Wolves.
Paul Pogba (thigh) remains unfit and the French midfielder has yet to play under Rangnick.
Aston Villa will be boosted by the return of England internationals Ollie Watkins and Tyrone Mings.
Wingers Trezeguet and Bertrand Traore are both on international duty in Cameroon, while Leon Bailey (thigh) and veteran Ashley Young (ankle) are doubts.
Villa have been busy in the transfer window, with a deal for Everton's Lucas Digne edging closer. Coutinho will not be available after Covid delayed his arrival but may make the league meeting between the two sides.
Predicted starting XIs:
Man United: Henderson, Dalot, Jones, Lindelof, Shaw, McTominay, Fred, Fernandes, Lingard, Greenwood, Cavani
Aston Villa: Martinez, Cash, Konsa, Mings, Targett, Ramsey, Luiz, McGinn, Buendia, Watkins, Ings
Aston Villa's need for a cup run looks greater
With the Red Devils facing tough opposition in Atletico Madrid in the Champions League, the fans will be keen to remain in the hunt for silverware on all fronts.
However, Rangnick may view it differently, with a top-four finish still the priority.
Aston Villa look to have banished any relegation concerns and will be able to give the competition their full attention.
With Coutinho set to bolster their attacking options and a winnable tie against Championship side Middlesbrough up next, their greater desire could prove the difference.