The 23-year-old has been heavily linked with a switch to the Etihad ever since Pep Guardiola took over as City boss in summer 2016, although the club refrained from tabling a formal offer.
The club lost out on another long-term defensive target, Virgil van Dijk, to Liverpool earlier this month when the Dutchman agreed a £75m move to Anfield, prompting Guardiola to reignite his interest in Laporte.
Yesterday it was claimed that City are willing to meet the Frenchman's £60m release clause and according to Marca, the player himself has now "reached the basis of an agreement" with the Premier League leaders.
The publication claims that Laporte will sign "a five-year contract" at the Etihad and the deal will be formally completed early next week.
The deal would make Laporte the second most expensive defender in history, behind only Van Dijk.