We want you to pick your best combined XI, using any formation (within reason) that you want.
So Roberto Firmino or Sergio Aguero? Alisson or Ederson? Kyle Walker or Trent Alexander-Arnold? You choose.
Share your results on social media using #bbcfootball.
What the fans think...
We asked one Manchester City fan and one Liverpool supporter to pick their combined XI. And they both came up with pretty evenly split line-ups that contained nine of the same players.
The only differences were at right-back, where both supporters picked the opposite team's player, and in goal, where they each selected their own club's Brazilian.
Nigel Rothband, host of The Man City Show Podcast, selected this XI...

A Manchester City fan's combined XI
"There is a toss-up at goalkeeper but I've gone with Ederson over Alisson," Rothband said. "He's a brilliant shot stopper, his distribution is outstanding and he plays as an additional defender.
"Robertson is an easy choice, he's probably the best left-back in the Premier League and it's an area City might have to strengthen in the transfer window.
"With Kyle Walker's drop in form over the past couple of weeks I've gone with the less experienced but hugely promising Trent Alexander-Arnold.
"I wouldn't use any Liverpool players in midfield as you can't get much better than the three I've chosen. While it's difficult to leave out Raheem Sterling I've gone for Mohamed Salah, who is an outstanding talent and Sadio Mane gets in just ahead of Leroy Sane."
And Liverpool fan Josh Sexton, of the Anfield Wrap, picked this team...

A Liverpool fan's combined XI
"Picking the defence was fairly straightforward," said Sexton. "The Brazil national team's coach has a decision to make between Alisson and Ederson and has mostly opted for the former, but Alisson has also been a revelation since he signed for Liverpool.
"Kyle Walker, I believe, is one of England's most well-rounded footballers. Andy Robertson has been a much more consistent option than anything City have had at left-back since Guardiola took over.
"The midfield was trickier, particularly looking at it from a Liverpool angle. The Reds have a pool of supremely talented midfielders. However, it would have been impossible to overlook the strength City have in the same department. Fernandinho is almost the perfect holding midfielder, Kevin de Bruyne is absolutely world class, and David Silva will go down as one of the best number 10s the Premier League has seen.
"The attack is the most difficult to choose. City fans will probably scoff and point towards their superiority in the 'goals for' column, but Mo Salah and Sadio Mane are absolutely crucial for Liverpool. While it was tough to overlook Roberto Firmino, Sergio Aguero is City's all-time leading goalscorer and one of the most well-rounded strikers the Premier League has seen."
And here's what the 5 live team came up with...
Commentator Ali Bruce-Ball: Allison, Robertson, Van Dijk, Laporte, Alexander-Arnold, Fernandinho, De Bruyne, Silva, Salah, Firmino, Aguero.
Commentator Guy Mowbray: Allison, Robertson, Van Dijk, Laporte, Alexander-Arnold, Fernandinho, De Bruyne, Silva, Salah, Sterling, Aguero.
Changing times?
When the teams met in January, only three Liverpool players made your starting XI, with eight Manchester City players included.
Forwards Mohamed Salah and Sadio Mane were included, along with then new signing Virgil van Dijk.
The £75m defender retained his place in October's combined XI alongside City captain Vincent Kompany - but another two Liverpool players were added, including left-back Andrew Robertson.

In January (left), only three Liverpool players made your starting XI. In October (right), there were five Reds players.
Brazilian goalkeeper Alisson also replaced City's Ederson, while Benjamin Mendy lost his place to Robertson.
Defensive midfielder Fernandinho came in for City team-mate Raheem Sterling in the most recent XI but David Silva, Kevin de Bruyne, Kyle Walker and Sergio Aguero kept their places.