This is according to The Metro, who further state that all four Premier League clubs have been tracking the £19.5 million-rated midfielder in recent times.
A former Real Madrid youngster, Niguez departed the Santiago Bernabeu for cross-city rivals Atletico back in 2008.
Although he is yet to make his mark with Diego Simeone's side, Saul has positively flourished this season during a prosperous loan spell with fellow La Liga outfit Rayo Vallecano.
An ever-present at the Campo de Fútbol de Vallecas, 19-year-old Saul has fully demonstrated his talent and ability to cope commendably at the highest level of Spanish domestic football.
Although the club are yet to appoint a new full-time manager to replace the hapless David Moyes, Manchester United are expected to be on the lookout for midfield reinforcements this summer.
With Louis van Gaal - who is expected to be appointed as manager at Old Trafford this week following the Netherlands' pre-World Cup friendly against Ecuador - noted for his ability to nurture young talent, Manchester United could be the perfect club for Saul.
Arsenal boss Arsene Wenger - whose side will contest the FA Cup final against Hull City at Wembley this afternoon - is also known to favour youth, with the experienced Frenchman never afraid to give the club's young players a chance to thrive in the first team.
If indeed both Manchester United and Arsenal are very keen to sign Saul soon, then they may have to move quickly with those same aforementioned reports suggesting that Liverpool may have already held preliminary talks with the player's father.