Martin Caceres flew to England from Italy yesterday for talks with Premier League clubs.
Southampton are interested in signing the Uruguay defender. He is a free agent after leaving Juventus last summer.
Caceres passed an AC Milan medical last week but failed to agree personal terms.
Milan chief executive Adriano Galliani told Mediaset that Caceres had “passed all of the medicals, but we could not agree personal terms.”
Caceres has been without a club since leaving Juve last summer, and the 29-year-old also came close to joining Crystal Palace last month.
Southampton boss Claude Puel is keen to fill the void left by Jose Fonte’s departure and Virgil van Dijk’s injury, with the club down to the bare bones for central defenders.