The Portuguese international was linked with a possible move to La Blaugrana last summer before eventually choosing to stay in Manchester in 2021/22.
City boss Pep Guardiola has previously hinted at his willingness to sell the former AS Monaco man if he is not happy with his squad role at the Etihad Stadium.
Silva is contracted to City until 2025, and the club could demand around €80m to sell him, due to his importance to Guardiola’s plans.
According to reports from Mundo Deportivo, a possible deal looks to be increasingly unlikely from within both parties, due to a lack of progress over a transfer.
Silva’s representatives are rumoured to have grown frustrated with the direction of negotiations with Barcelona keen to avoid a repeat of a last minute rejection from the 27-year-old this month.