The 23-year-old, who is a key member of Marcelo Bielsa’s side, has already been looked at by several Premier League clubs.
However, according to The Sun, United have sent assistant manager Mike Phelan and coach Kieran McKenna to look at Phillips on at least two separate occasions.
The report claims Phelan visited Elland Road for the Whites’ 1-0 victory over Birmingham last Saturday, in a clash where Phillips scored the only goal of the game.
It is claimed that United then followed this up with another visit a few days later, but this time McKenna made the trip, when the Yorkshire club travelled to Deepdale to take on Preston North End.
Phillips is often played as a holding midfielder role as part of Bielsa’s preferred 4-1-4-1 formation, but does have the ability to dictate the tempo of the game, as well as having the threat of a long range shot.
But United are aware they are likely to have to spend a lot of money if they want to pry the player away from their bitter rivals, especially as the youngster recently signed a new long-term contract with the club.
During the summer Leeds rejected a £27million bid from Tottenham and while other Premier League clubs, including Aston Villa, Sheffield United, Wolves and Burnley were all reported to be monitoring the player, Leeds made it clear they had no intention of selling.