FJ Diaz of Spanish daily AS (h/t Will Giles of Metro) claimed that the Premier League giants will compete for Atleti's breakout star, who has shone since a successful loan spell at Rayo Vallecano last year.
The Spain under-21 international is currently tipped to make his bow for the full national side in due course, tempting United and Arsenal to watch the player more closely.
Saul is contracted to Diego Simeone's team until 2020, according to Diaz, but his father revealed that his son could leave due to the inclusion of a release clause in his current deal. Turkish giants Galatasaray are also said to be tracking the player, but Arsenal and United are "leading the race" to capture him.
The Elche-born talent joined the Rojiblancos' youth team in 2010 and has progressed through the ranks to become one of Simeone's automatic selections.
The 21-year-old has featured 28 times for Atletico in La Liga and the Champions League this season, according to WhoScored.com.
The Daily Mirror claimed Saul has turned down a new deal from his club, and United have scouted the midfielder over a period of a year. The Spaniard has developed a reputation for his defensive attributes but is equally happy positioned further up the field or on the flanks.
Saul is also adding goals to his burgeoning skill set, as highlighted by Opta Jose:
7 - Saúl Ñíguez has scored seven goals for @atletienglish this season, as many as Fernando Torres (4) and Luciano Vietto (3) combined. Anvil2016-3-1 21:10:36
Sky Sports’ Spanish football expert Guillem Balague recently confirmed the interest from United but added that Simeone was not looking to sell in January:
Guillem Balague @GuillemBalague
The truth is that there has been an approach. United offers €20m but Atletico not selling ATM https://t.co/anOfjFWPFn2016-1-11 14:55:31
Saul is the type of player Gunners coach Arsene Wenger gravitates towards; he is versed in possession football and can play in a number of roles through the middle of the park.
Arsenal are desperate to find a defensive entity who can run the engine room in midfield and also support Wenger's plethora of attacking individuals.
Here is a video displaying Saul's ability:
If the Gunners lose out to United in their pursuit of Saul, they could turn their interests towards long-term target Ilkay Gundogan of Borussia Dortmund.
According to German newspaper Bild (h/t talkSPORT,) BVB are ready to sell the German international star, with his deal having less than 18 months to run. Gundogan is valued at £23 million and is also wanted by Barcelona and Juventus.
The player has helped Dortmund find their feet in the Bundesliga after a disappointing campaign last year, but his refusal to sign a new deal could see him exit the Westfalenstadion.
Artur Petrosyan @arturpetrosyan
Juventus are now also in for Ilkay Gundogan. Them, Real Madrid and Liverpool will all try to sign him in the summer.2016-2-18 09:05:39
Gundogan has similar qualities to Saul but is vastly more experienced than the young Spaniard.
However, the German has suffered from injury through his career and could potentially spend time on the touchline if his health collapses once again.
Saul is the player Wenger should target in the summer, and his buyout clause is not unreasonable in the current market.
The Spaniard would add steel and vitality to Arsenal's midfield as he becomes one of Europe's most prized individuals.