Both sides are said to be keen on the defender as they are likely to see players in that current position leave during the summer.
At Stamford Bridge, Felipe Luis in particular is said to be keen on a return to former club Atletico Madrid, per the Evening Standard, having failed to establish himself in the Premier League, with Cesar Azpilicueta ahead of him in the first team.
At the Etihad, both Gael Clichy and Aleksandar Kolorov both compete for the left-back spot, but the Serbian has been linked with a move away, with several sides in Serie A thought to be interested in him, according to the Mirror.
Any move for Ghoulam would be a relatively cheap one for both clubs as well, with the Italians thought to be willing to accept a bid of €15million for their man, around £10.8million.
They would, however, face competition for his services, with La Liga giants Real Madrid and new manager Rafa Benitez, who managed the player at Napoli last year, keen on him also.