Liverpool got their recruitment underway even earlier than their old foes, agreeing a deal to sign Ibrahima Konate from RB Leipzig back in May before he officially joined Jurgen Klopp's side on July 1.
But it could be argued that the signing of a centre-half came a year too late, with the Reds opting not to replace Dejan Lovren last summer - and then paying the price as an unprecedented injury crisis swept through Klopp's squad and derailed their title defence.
United took advantage of Liverpool's woes, mounting an impressive unbeaten run to eventually finish second in the Premier League.
Man Utd boss Ole Gunnar Solskjaer is expected to target midfield improvements (Image: GETTY)
Solskjaer's side faced criticism for their transfer activity last summer, signing only Donny van de Beek before their deadline day swoops for Edinson Cavani and Facundo Pellistri.
But their refusal to meet Dortmund's exhorbitant price tag for Sancho looks set to have paid dividends, with the winger joining for £35m less a year later - ensuring United have money left over to land a top-class centre-back in Varane.
The pair have been described as 'statement' signings, with the Red Devils appearing to be on an upward curve as they look to challenge Manchester City for the title next term.
Liverpool, of course, will come back stronger following the disappointment of failing to defend their crown - as evidenced by their impressive surge at the end of last season to ensure they didn't miss out on a Champions League place.
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy
But United could make another big statement about the rate of their progression if they beat Liverpool to the signing of Saul.
And they could have an advantage over their rivals, after Atletico boss Diego Simeone outlined what the 26-year-old wants from his next challenge.
In an interview with Spanish publicationDiario ASlate last month, Simeone said Saul is keen for role at the centre of the team in which he can dictate play.
"Last season he spoke with the club, with us about his needs and what he spoke about was the option of having a position on the pitch where he feels more important," said the manager.
Do you want an exclusive pre-season preview for YOUR club - both in your inbox and through your letterbox? Head over here to find out more and secure your copy.
Atletico Madrid midfielder Saul Niguez is reportedly a target for Man Utd and Liverpool (Image: GETTY)
"And I consider that Saul became Saul by playing everywhere, but he or many of those around him see it as something negative."
Such a role could be available at United, with Solskjaer believed to be planning on utilising a 4-3-3 formation in which midfield spots could be up for grabs.
Bruno Fernandes is likely to be a nailed-on starter, but Van de Beek has so far failed to carve out a role for himself, while uncertainty continues over Paul Pogba's future.
Fred faced plenty of criticism last season and could lose out if United sign a new midfielder, while Scott McTominay would surely benefit from increased competition.
Liverpool, by contrast, are stacked with midfield options despite having seen Gini Wijnaldum depart, with Jordan Henderson, Fabinho, Thiago and the emerging Curtis Jones among the leading options vying for places.