Pep Guardiola has zeroed in on England international Phillips as the player he wants to come in and replace the departing Fernandinho.
Phillips has been strongly linked with a move away from Elland Road and Manchester City are working on a swoop to snap him up.
The Citizens are now close to agreeing personal terms with Phillips, according to Italian broadcaster Sportitalia.
And discussions with Leeds are also progressing in the right direction, with Manchester City having made a proposal of £45m plus bonus payments.
It is suggested that Leeds are looking for £60m to let the England international depart.
Leeds are moving to complete the capture of Marc Roca from Bayern Munich, but it has been suggested the midfielder is not seen as a replacement for Phillips.
The Whites could also lose the services of winger Raphinha this summer, with the Brazil international wanted by Barcelona and several Premier League clubs.