Palace have turned their attention towards the France international centre-back after failing to secure the services of Mamadou Sakho from Liverpool, according to the report.
Liverpool are claimed to want as much as £30m in order to part company with 27-year-old France international defender Sakho.
Mangala joined Premier League giants City from Portuguese powerhouse FC Porto in the summer of 2014 for a transfer fee reported by BBC Sport to be worth £32m.
Much was expected of the Frenchman when he arrived at the Etihad Stadium, but he has failed to make a massive impact and spent the 2016-17 campaign on loan at Spanish club Valencia.
Palace have made a disappointing start to the 2017-18 Premier League campaign and have lost all three of their league fixtures so far.