Cech has been dropped to bench this term thanks to the return of Thibaut Courtois, who previously spent three successful loan spells at Atletico Madrid.
The 32-year-old enjoyed 10 relatively unchallenged years at Stamford Bridge, but is now becoming frustrated at his limited game time.
According to reports in Italy, the Giallorossi are currently in talks with the Blues over a possible transfer deal to be completed in the winter window.
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The Serie A giants are looking for a replacement for Morgan De Sanctis, who turns 38 in March.
If the deal goes ahead, Cech would join former Chelsea team-mate Ashley Cole at the Stadio Olimpico, who moved there in the summer on a free.
The Czech Republic goalkeeper has made just two outings this term, starting once in the League Cup.