French publication L'Equipe (h/t Metro's George Bellshaw) reported on Thursday the alleged meeting last week, during which United were said to have made their ambition to bring Guardiola to Old Trafford clear.
The same report stated Manchester City remain the favourites to hire the former Barcelona chief in the summer, but United can make a strong case for Guardiola to choose them over their neighbours.
In terms of history, the Red Devils have a tradition of playing expansive, attacking football. It's a style compatible with Guardiola's philosophy.
He's also likely to find the Old Trafford club's track record of developing and giving chances to young players appealing. From the Busby Babes and the Class of '92, United have never been shy about building successful sides on a foundation of youth.
Guardiola did the same when he brought Sergio Busquets and Pedro through at Barcelona. The Spaniard has also recruited young stars such as Douglas Costa and Thiago Alcantara at Bayern.
Although they can't quite match the spending power of City, United are certainly no slouches in the market.
But there are reasons to believe Guardiola will perhaps choose another Premier League suitor over the Red Devils.
City's lack of history as a European superpower could appeal to the manager, according to James Robson of the Manchester Evening News: "Then there’s City—still something of a blank slate in the age of the [UEFA] Champions League. A club ready to let a manager like Guardiola mould it in his own image. Ready to let him write his own history—and with the resources to make his wildest ambitions become reality."
Like United, the Gunners' recent history of stylish, attacking football and faith in youth under manager Arsene Wenger makes the north London club a great fit for Guardiola.
The Spaniard has indicated it could be up to two years before he manages in the Premier League, per Sky Sports' Peter Gilbert. That would put him in line to succeed Wenger when the Frenchman's current contract expires in 2017.
Guardiola's future has been the subject of intense speculation since he declared his intention to step down from his job with Munich at the end of this season. Since then, the pressure has increased on a host of managers in England's top flight, including United's Louis van Gaal.
Guardiola has apologised for the storm his decision has caused, according to BBC Sport.
But United fans would likely not forgive their club for missing out on possibly the most sought-after manager in Europe.