Napoli president Aurelio De Laurentiis says the club are in talks with Swansea over a deal to sign Michu, although an agreement has yet to be reached.
The 28-year-old, who joined the Swans from Rayo Vallecano in 2012, suffered with injuries last season and scored just two goals in 15 league starts.
The Premier League side are now willing to let go of a player who shined in his debut campaign, and Michu did not travel with the squad to the United States for a preseason tour due to the talks with Napoli.
According to reports, the Serie A club want Michu on loan, although the Swans are keen on a permanent deal.
"Michu? Negotiations are well under way for months but there is still no agreement reached," De Laurentiis is quoted as saying by BBC Sport.
Pablo Hernandez, Jose Canas and Alejandro Pozuelo all missed Swansea's trip to the United States as well.
Hernandez is nearing the last year of his contract, while Canas and Pozuelo are reported to be deemed surplus to requirements by manager Garry Monk.