Jack Grealish, James Maddison and Jude Bellingham have all been touted as possible targets for one of Ole Gunnar Solskjaer's priority areas ahead of the upcoming window, but reports from Spain suggest that they have instead settled on Saul.
The 25-year-old has regularly been linked with a move to the Premier League despite signing a nine-year contract which keeps him tied to Atletico until 2026.
The Spanish outfit initially wanted £131m before considering his sale, but the coronavirus pandemic has reportedly forced them to lower that asking price to around £70m, bringing Saul into a similar price range as United's other targets.
Here, Sports Mole looks at what shirt numbers could be available to Saul should he move to Old Trafford.
Saul has been firmly entrenched in the number eight shirt for Atletico over the last four seasons, but that is currently taken by Juan Mata, who has been United's '8' for six-and-a-half years since joining from Chelsea.
The Spaniard is not likely to leave Old Trafford this summer and still has a year remaining on his contract, with the option of a further 12 months on top of that which the Red Devils are likely to trigger if past examples are anything to go by.
The only realistic way Saul would be granted the United number eight is if Mata willingly steps aside, then, but a more likely scenario is the newcomer taking on a different number.
The most notable one available is the iconic '7' jersey, which has previously been worn by George Best, Bryan Robson, Eric Cantona, David Beckham and Cristiano Ronaldo and was most recently taken by Alexis Sanchez, who is currently on loan at Inter Milan.
Sanchez is expected to leave Old Trafford this summer, or at the very least give up the number seven shirt, but that has already been promised to another transfer target in Jadon Sancho, according to reports.
The number 11 is also available but is more associated with left wingers than central midfielders, while the numbers four and six, currently occupied by Phil Jones and Paul Pogba respectively, would become options should either leave the club this summer.
Before being promoted to Atletico's '8', Saul wore the number 17 in the Spanish capital, although that is also taken at Old Trafford by the ever-improving Fred as things stand.
Other currently unclaimed numbers include '12', '16' and '19', although even the first two of those previously belonged to players who are only out on loan at the moment.