City are believed to be open to allowing the 28-year-old to leave the Etihad when the transfer window opens next month.
The former Leeds star has a host of Premier League clubs linked with him, including the likes of Liverpool and Newcastle.
Now Manchester United could consider making a shock offer for him to switch from the blue to the red half of the city.
Phillips has played just 89 minutes in the Premier League this season, making just four substitute appearances.
Pep Guardiola admitted this week that the midfielder does not fit into his plans.
Read more on transfers
Man United to poach Newcastle chief, Palhinha transfer, ex-Premier League boss to Forest?
Sancho free to leave Man United in January and linked with swap for Borussia Dortmund star
"I don't know what's going to happen [in January]," Guardiola said. "I feel so sorry for my decision for him. I've said that many times.
"He doesn't deserve what has happened to him and I'm so sorry.
"The only thing I can say about him is I am asking for good personalities and characters and he is a perfect example. And after that I have to give him something and I didn't do that.
"It's just because I visualise some things and visualise the team and things - and I struggle to see him.
Most read in Football
'It's his job!' - Roy Hodgson gets slammed for tetchy talkSPORT interview
Harry Kane and Co refuse to speak after Bayern humiliation, but Man United get warning
Bloodied Martinez pumps up Villa Park crowd after taking boot to the eye in iconic scenes
Villa match stunning 90 year old record and Arteta looks on in despair as Arsenal defeated
"I'm not very pleased [with myself] and I am so sorry for him. I will not say that [to him] because it is a business and I have to be a professional.
"But if one guy behaves [poorly], I don't care. But the way he behaves with the team-mates and everyone, I care. So that's why hopefully it can turn around.
"And I've said many times, if it comes to January and he stays, I'm more than pleased because he trains really good and he's a lovely guy and character."