The 23-year-old centre-back - who has been at Athletic Bilbao since he was 16 - would cost City £57million (R964-million) owing to a release clause in his contract at Bilbao but would resolve a problematic area for manager Pep Guardiola where veteran Vincent Kompany is injury-prone and Frenchman Eliaquim Mangala has not impressed.
Laporte - whose move reportedly would be dependent on Mangala moving on - would provide cover for present first-choice pairing England global John Stones and Argentinian Nicolas Otamendi.
The deal of the French player would also end City's perusal of West Brom central defender Jonny Evans who had been closely linked with a move to the Etihad Stadium.
City's current transfer record is £55million. The transfer would eclipse the Citizens biggest ever outlay for a player which now stands at £55m paid to Wolfsburg for midfielder Kevin de Bruyne in the summer of 2015.
Guardiola has always been interested in Laporte, having failed to make a solid move during his team at Bayern Munich and previously, with Barcelona. Manchester City now has a 12 point lead at the top of the Premier League and are set to take on Cardiff City in the 4th round of the FA Cup on Sunday.