The two clubs currently fill the top two positions in the Premier League and in January, both were keen to reinforce their squads for the second half of the season.
City and Pep Guardiola were desperate to add Arsenal's Alexis Sanchez to their forward line, but baulked at his financial demands.
This allowed Jose Mourinho and United to swoop in, with the Red Devils completing the biggest winter transfer probably ever seen yesterday.
Now, City have to act fast in order to add to their squad, with Shakhtar Donetsk's Fred reportedly close to a switch to the Etihad.
One man who started cropping up on Tuesday was Athletic Bilbao defender Aymeric Laporte, with City expressing their interest in the Frenchman in earlier windows.
Sky Sports are reporting that City are prepared to pay up to £60m for the highly-rated defender, who has had some serious issues with injury in the past few seasons.
Is he worth that much? Some will be skeptical, but one person who will not be is United legend Gary Neville.
The Sky Sports regular took to Twitter to voice his opinion on the defender who he faced three times during his short stint in charge of Valencia.
It makes for some interesting reading.
So, Neville thinks Laporte is worth the money being quoted.
The £60m fee - which is his release clause - would make him the second most expensive defender of all time, with the £75m Liverpool forked out for Virgil van Dijk the only other deal that would top it.
Laporte is a full French international and was only allowed to feature for Bilbao after being invited for a trial by the club after a scouting mission in 2009.
He would be seen as the ideal man to replace Vincent Kompany, with the Belgian defender's injury record far too much of a hindrance to Guardiola's side.
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