The 26-year-old made his first-team debut for the Whites in 2015 and has gone on to feature 234 times in all competitions for the club.
During this period he has been touted as one of England’s best defensive-midfielders and now City are ‘confident’ Phillips will ‘push’ to leave West Yorkshire for Manchester this summer, according to The Athletic.
The site claims the Sky Blues have a price range in mind for the 26-year-old and will look to pursue a deal for the midfielder once he has finished international duty with the Three Lions.
A move for Phillips would make sense for City with the departure of Fernandinho this summer.
If the rumours are true, then it shows Pep Guardiola’s side mean business during the transfer window.
The Catalan has already recruited sought-after forward Erling Haaland for £51.1m from Borussia Dortmund, while also acquiring Julian Alavarez in January - the latter is expected to join up with the Sky Blues squad for pre-season.
To add to this, City chairman Khaldoon Al Mubarak indicated last month that the club will be active in the market this summer.
“I can confirm that there will be more players coming in,” he told the Sky Blues’ website.
“We are looking to strengthen the team in the areas that we need strengthening. As you know, every season some players leave, and then we have to continuously refresh the team.
“Again, we will always look at improving and strengthening. I think we’ve made two very important additions already, but I anticipate we’ll be doing a couple more.
“We’ll try to go as fast as we can, but you know how the market goes. It’s not always entirely in our control.”
City will be heading into next season with the aim of winning the Premier League for a third consecutive campaign - something only their cross-town rivals Manchester United have been able to achieve.