Stones, 32, made only four Premier League starts last season and announced in April that he would not be extending his decade-long stay at the Etihad Stadium. He leaves Manchester City having won 19 major trophies with the club.
"I lived out all my dreams and lifted all the things I came here to achieve," Stones said at the time of his announcement.
Inter Milan's interest has emerged via German outlet Bild, with the Serie A champions potentially needing cover after Stefan de Vrij, 34, and Francesco Acerbi, 38, are expected to leave this summer. The club had been tracking Udinese defender Oumar Solet, 26, but that interest is reported to have cooled.
Juventus have also had Stones on their radar, and now face potential competition from their Italian rivals for his signature.
How Stones views his next move is not yet known, with no formal negotiations reported with any club. The 32-year-old has options across multiple leagues and will take his time deciding where he continues his career following the World Cup, where he is part of England's squad.
The timing of Inter's reported interest aligns with their defensive planning. With two experienced centre-backs potentially departing and their pursuit of Solet cooling, a free transfer for a player of Stones' quality would represent practical and cost-effective recruitment for the Serie A champions.
Stones' availability without a fee is likely to generate further attention from clubs across Europe in the coming weeks, particularly given his experience at the highest level across a decade at one of the Premier League's dominant clubs.