The 32-year-old, formerly a first-team regular at Chelsea, has made just five league appearances this season after being dislodged from the number one spot by Thibaut Courtois, and looks likely to be available at the end of the season.
British newspaper the Daily Star claims that both Inter and Roma are interested in securing his services but Southampton are especially keen.
The Saints recently lost Fraser Forster to a long-term injury and are on the look out for a new keeper, with Cech reportedly fitting the bill.
Current Nerazzurri number one Samir Handanovic has yet to sign a contract extension at the San Siro prompting speculation that he may be sold come the summer, leaving coach Roberto Mancini to assess potential new recruits.
The Giallorossi, who have been linked with Handanovic, are looking to find a successor to veteran Morgan De Sanctis who looks likely to be second-choice next season, and Cech may be an option.