The 6ft 4in defender is rated at £30m by the current Brazilian league leaders, having attracted interest from a host of other top teams in Europe.
La Liga giants Barcelona, however, do have a first option on the player which would allow them to purchase Mina for £9m next summer.
The Catalan outfit would have to pay £10m in 2018, or £12m in 2019, should they decide to delay their decision any longer.
It's believed the Citizens, who paid Palmeiras £28m for striker Gabriel Jesus, also like what they see in Mina.
Go-betweens have attempted to discover if there are any get-out clauses which could yet see Palmeiras buy-out Barcelona's option.
City boss Pep Guardiola wants to recruit another young central defender next summer due to the continued fitness concerns over his skipper Vincent Kompany.