The Argentina international, predominantly a centre-back, would reportedly cost City around £4m and provide them with a veteran replacement for Kolo Toure, who left for Liverpool earlier this summer.
Boss Manuel Pellegrini is seeking reinforcements at the back, with Vincent Kompany likely to miss the next six weeks and Matija Nastasic only just back after a hamstring injury.
The Chilean was interested in Real Madrid's Pepe but now turns his attentions to a player he knows well from their time together at Malaga.
Demichelis only signed for Atletico two months ago after the expiry of his deal with Malaga, for whom he played 83 times, scoring eight goals.
The 32-year-old played nearly 250 times in Germany for Bayern Munich and has 37 caps for his country.