For a long time the Red Devils have been linked with Declan Rice as they look for the holding midfielder who can be the next step in their team-building. But an increasing number of reports suggest they have given up on the idea of the West Ham United midfielder, believing him to be over-priced, and turned to Phillips instead.
With big clubs usually doing most of their business in the summer windows, it could be some time before a bid lands at Elland Road, but whoever has dropped the information into the media could be just starting the process of testing the water.
If they have been scared off by West Ham's price - reported in some quarters to be £90m - they may not find Phillips is a much cheaper option.
The huge amount of money spread across England's top flight means all its clubs have the financial wherewithal to fight off predators, as Tottenham Hotspur did to Manchester City this summer, although often it boils down to the player's attitude. Whether holding onto Harry Kane proves to be a laudable or regrettable move only time will tell. Phillips is under contract until 2024 and a passionate fan of the club.
As their Premier League win record with and without him shows, he is also a key part of Leeds's team and has been ever since coach Marcelo Bielsa arrived in West Yorkshire and converted the box-to-box midfielder into a holding player and deep-lying playmaker.
As a Leeds boy, his symbolic worth to Leeds is greater still.
The apparent interest from the down the M62 shows how Phillips's reputation has rocketed in the last six months.
During the European Championships he established a midfield partnership with Rice that made him fundamental to a team which reached the final, and was named England's player of the season.
As a boyhood Leeds fan, Phillips will no doubt be aware how controversial transfers from Elland Road can be. Last month Rio Ferdinand was loudly and persistently abused by away fans still unhappy about his 2002 move when Leeds played at Old Trafford. Eric Cantona, Alan Smith, Gordon McQueen and Joe Jordan are some of the others who made unpopular moves.
Not that Leeds have not benefited too. Frustrated at a lack of opportunities in Manchester, Jonny Giles became one of Leeds's greatest midfielders and Gordon Strachan captained their last title-winning team after being deemed surplus to requirements by Alex Ferguson.