The club chairman, Huw Jenkins, has revealed the striker is a target for the Serie A side, with negotiations ongoing with his agent, with both a loan or permanent move possible
The Spaniard has been strongly linked with a move away from the Liberty Stadium in recent weeks, and did not travel to the United States for the club's pre-season tour.
Jenkins has now revealed talks have taken place regarding a potential switch to Serie A.
"Napoli have enquired about Michu and we have been talking to them and to Michu's agent," he is quoted as saying by the South Wales Evening Post.
"But there are other options and nothing is finalised yet."
When asked whether the talks involved a loan or permanent deal, Jenkins added: "We are discussing various options."
Michu arrived in south Wales for a fee of £2.2 million from Rayo Vallecano in 2012 and scored 18 Premier League goals in his first season.
However, the 28-year-old endured an injury-plagued 2013-14 campaign, making just 15 top-flight starts.