Phillips is keen to make the switch to St James Park but City are looking for a loan fee of at least £5million and an obligation to buy.
Juventus also have England midfielder Phillips on their list of January targets, along with Fulham.
Newcastle want Phillips to replace the banned Sandro Tonali, but do not have the funds to do a permanent deal.
The former Leeds captain has played less than 90 minutes of Premier League football this season.
talkSPORT understands City have given Phillips a green light to leave the club this month.
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The 28-year-old appeared to wave goodbye to the club's travelling supporters after netting his first goal for City in the recent Champions League win over Red Star Belgrade.
City paid £42m to sign Phillips from Leeds in the summer of 2022 after a standout year for club and country.
Phillips started every game for England at Euro 2020 and became one of the Premier League's most sought-after midfielders.
But Phillips was unable to challenge Rodri for a place in City's quadruple-winning team and spent most of the 2022/23 season on the bench.
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Even in the rare absence of Rodri, manager Pep Guardiola preferred alternative options, such as academy right-back Rico Lewis.
Phillips' future at the club looked increasingly bleak as City spent a combined £77million on Matheus Nunes and Mateo Kovacic last summer.
Manchester City's Kalvin Phillips discusses the difference in tactics implemented between former manager, Marcelo Bielsa and Pep Guardiola