The Argentine took over at the Premier League club last month following the surprise departure of Nigel Adkins.
"Me on a Serie A bench? I like Italian football, I also have relatives in Italy," Pochettino is quoted as saying by tuttomercatoweb.com. "In the future, why not?"
Pochettino has guided the 15th-placed Saints to one win, two draws and one defeat during his first four matches in charge of the side.