Both clubs are reportedly in the market for a new left back, with Jurgen Klopp and Manuel Pellegrini not impressed with their current options.
And their eyes have fallen on Hammers star Aaron Cresswell, with him continuing to impress under Slaven Bilic this season.
The left back has been highly impressive since arriving from Ipswich at the beginning of last season and could be a surprise contender to head to Euro 2016 with England if he keeps up his good form.
Liverpool would be interested in a move in January, but City are happy to wait until the summer, potentially when they have a new man in charge, before trying to sign him, reports the Times.
In the case of the latter, they are particularly keen as they are looking to add homegrown talent to their squad in order to comply with Premier League and UEFA’s homegrown quotas.
Cresswell would not likely come cheap though, with the Hammers sure to ask for big money for a player who only signed a new five-year deal in June last year.