The 25-year-old joined City from Athletic Bilbao in January 2018 and has made 72 appearances for the English champions in all competitions.
The Frenchman has been restricted to just eight outings this term due to a serious knee injury, though, and Pep Guardiola's side have struggled defensively in his absence.
Laporte has a contract at the Etihad Stadium until the summer of 2025, but according to Mundo Deportivo, Barca are considering a move in this summer's transfer window.
The report claims that the Spanish champions will attempt to use City's two-year European suspension to land the centre-back ahead of the 2020-21 campaign.
As it stands, the Citizens will be unable to play in the Champions League until the 2022-23 season due to a UEFA ban, although the club have appealed the decision. body check tags ::