The French defender, who has impressed since moving to the Camp Nou in 2016, is contracted to the club until the summer of 2021 but has a release clause of €60m (£53.4m).
A recent report suggested that Pep Guardiola has made the Umtiti one of his top defensive targets with the Spanish coach said to be planning a move during the January transfer window. City were said to be ready to meet the defender's release clause and take him to the Etihad Stadium.
Apart from City, Manchester United are also said to be interested with Jose Mourinho looking to bolster his defence. The La Liga leaders are keen to hold on to the highly-rated defender, especially since they are likely to lose experienced veteran Javier Mascherano to Chinese Super League club Hebei Fortune this month.
The 24-year-old defender, who is currently side-lined with a hamstring injury, is around a month away from returning to action. He has formed a strong partnership with Gerard Pique and established himself as the first choice centre-back alongside the Spaniard.
According to Football Espana, via Spanish daily Marca, Barcelona are keen to offer him a new deal and increase his release to ward off potential suitors. The report claims that the defender remains committed to the Spanish club, but in the wake of Virgil van Dijk's £75m – a world-record for a defender – move to Liverpool, the Catalan club are not willing to take a risk and leave them in a vulnerable position.
It is claimed that the club will open talks with the defender and his representatives in the coming weeks with regards to a lucrative new deal.