Hernandez instead signed with Bayer Leverkusen after being deemed surplus to requirements at Manchester United on his return from a loan spell at Real Madrid.
The Mexican striker has revived his career in Germany with 17 goals in 26 games.
"Juventus, Inter, [AC] Milan, Lazio and Roma tried to sign me in the summer," Hernandez told La Gazzetta dello Sport.
"I picked Leverkusen because of the Champions League and they made me feel wanted. They were convinced I could help them improve and that made me smile.
"Leverkusen have exercised an option for me and I have a contract until 2018. I have everything I need here.
"I've played for three clubs in three different countries so I know that anything can happen. Serie A is a great league, I can't exclude playing there."