The 26-year-old has spent his entire career at Elland Road, making a total of 234 appearances in all competitions.
However, it has been widely claimed that the England international is now open to taking on a new challenge as Jesse Marsch reshapes his first-team squad.
A recent report has claimed that direct talks between the relevant parties are due to take place with City in a position to meet Leeds' asking price.
However, according to Football Insider, the Premier League champions face competition in the form of West Ham and Aston Villa.
Despite the differences in domestic and European pedigree, both clubs would realistically provide Phillips with more appearances from the starting lineup.
The Hammers manager is allegedly keen to bring in two fresh faces to compete with his established pair, particularly with Europa Conference League football also on their agenda.
Villa have far more competition for places in the centre of the pitch, but Phillips would almost certainly command a place in Steven Gerrard's starting lineup.
Nevertheless, it is claimed that Phillips intends to sign for Man City if terms can be finalised between the two clubs over the coming weeks.
City are expected to pay in the region of £50m for a player who has just two years remaining on his contract and endured an injury-hit campaign during 2021-22.
That said, Phillips still managed to make 18 starts and two substitute appearances in the Premier League, completing the 90 minutes in Leeds' final six fixtures.
At the same time as handling the future of Phillips, Leeds are also receiving interest in fellow key man Raphinha, with Arsenal said to have failed with their opening approach for the Brazilian playmaker. body check tags ::