City boss Pep Guardiola, who is a long-time admirer of the 23-year-old, is looking to sign another defensive player, with Vincent Kompany unreliable through injury and Eliaquim Mangala failing to justify his £42m transfer fee.
According to The Sun, Guardiola is focused on Laporte as the ideal remedy to his problems at the back, and is prepared to spend big to secure the Frenchman's signature.
Laporte, who moved to Bilbao in 2010, made his senior debut two years later. The centre-back has made 27 appearances for the Spanish side this term, scoring one goal.
Chelsea, Barcelona and Paris Saint-Germain are also allegedly keen on Laporte as an option at the back.