Despite winning the Premier League title last season, manager Pep Guardiola used a number of different players at left-back.
While City are well stocked for options on that side of the pitch, it has been suggested that Benjamin Mendy could depart the Etihad Stadium in the coming weeks.
According to Portuguese journalist Pedro Almeira, City have instigated discussions with regards to the availability of Grimaldo.
The 25-year-old, who came through the Barcelona academy system, has made 169 appearances in all competitions since moving to Benfica in 2016.
The Portuguese giants are said to be demanding in the region of €30m (£25.6m) for a player who has two years left on his contract. body check tags ::