A central defender is expected to be high on the agenda for the Citizens after Pep Guardiola has been left short in that position this season.
Midfield duo Fernandinho and Rodri have had to fill in due to injuries picked up by Aymeric Laporte, John Stones and Nicolas Otamendi.
Inter Milan defender Milan Skriniar is understood to be City's first choice after some impressive displays in Serie A.
The Slovakia international is comfortable on the ball and would suit Guardiola's style. However, Inter are unlikely to let him go without a fight, especially midway through the season.
City were reportedly considering making a move for the 24-year-old in the summer following Vincent Kompany's departure.
Leicester's Caglar Soyuncu is another potential option and City have been long-term admirers of the Turkey international.
Reports claim he turned down a move to the Etihad in favour of signing for Leicester in August 2018 due to fears over a lack of game time at City.
That decision appears to have worked in his favour after becoming a regular at King Power Stadium but his performances have only further piqued City's interest.
Looking further up the field, Juventus' Rodrigo Bentancur is still on City's radar although Barcelona are also keen on the £35million-rated midfielder.
The 22-year-old hasn't figured as a major part of Maurizio Sarri's plans in Turin and a move away could be on the cards.
Reports in Spain claim Isco could be targeted by the Premier League champions in January as Guardiola looks to find a long-term successor to David Silva.
Silva is set to leave the Etihad when his deal expires at the end of the campaign and Isco is seen as the perfect replacement.
Isco was restricted to just 11 starting appearances in La Liga last season and Real Madrid aren't expected to stand in his way if the price is right.