Correio de Manha says City boss Pep Guardiola is preparing a mega £86million (€100m) bid for the 25-year-old, which would see Fernandes join the club at the end of the season.
Rivals United have been chasing a deal for Fernandes since Christmas.
The Red Devils were also very close to finalising a move for the Portugal international last week.
But, talks stalled over the transfer fee, with Sporting demanding £68m up front. United were only willing to pay £50m, with a further £15m in add-ons.
A shock move for Fernandes would make sense for the current Premier League champions.
They're set to lose David Silva at the end of this season, after a 10-year stay at the Etihad Stadium.
There will be a vacancy in centre-midfield for Guardiola's side, and Fernandes would fit straight into Guardiola's system.