With newly-appointed boss Erik ten Hag at the helm, United are expected to sign at least one new centre-back this summer, a response to a poor season and a number of players likely to head out of Old Trafford.
The defensive trio of Eric Bailly, Phil Jones and Axel Tuanzebe could all join new clubs over the coming weeks, departures which would leave United with just three players for the middle of their backline.
However, if reports are to be believed, Ten Hag is ready to be proactive in the search for replacements with Villarreal's Pau Torres and Ajax's Jurrien Timber both on his radar.
Nevertheless, according to The Telegraph, United may also make a formal approach for Gvardiol, a player known to have admirers in Chelsea.
When it was suggested that Chelsea may move for the Croatia international, reports quickly followed that RB Leizpig had no intention of parting ways with a prospect who they only signed last summer.
Furthermore, the 20-year-old has already established himself as a key man, making a total of 40 starts and six substitute appearances during his first campaign.
With four years still remaining on Gvardiol's contract, that appears enough to leave United and Chelsea as clear outsiders to get a deal over the line for 2022-23.
Much could depend on whether either club are prepared to pay almost treble what Leipzig paid 12 months ago, said to be somewhere in the region of £17m.
That may leave both teams to look elsewhere, particularly when there are other players on the market for similar value with more big-match experience.
Torres falls into that category, the 25-year-old having recently starred for Villarreal during their run to the Champions League semi-finals and there seemingly being scope for business to be done at below his €55m (£47.08m) release clause.
In the case of Timber, the 20-year-old has previously worked with Ten Hag at Ajax, the versatile youngster being provided with 38 appearances last season.
Netherlands manager and former United Louis van Gaal has talked up the prospect of Timber representing the Premier League giants, claiming that he has already reached the level required to play at the Theatre Of Dreams.