The Spanish striker isn't expected to join his Swansea teammates as they fly off on their pre-season tour of the USA today.
It is widely believed that the injury-troubled Spaniard doesn't feature in manager Garry Monk's plans for next season and his time at the Liberty Stadium could be drawing to a close.
Napoli are trying to add some strength in depth after falling short of the title pace in Serie A last term and going out at the group stage of the Champions League.
Napoli boss Rafa Benitez is said to like the idea of adding someone to his squad who can take the pressure off Gonzalo Higuain and also play a wide role.
It is suggested that Swansea may be happier to sell Michu outright, so it could be difficult for Napoli to persuade the Welsh club to come to an arrangement.
There may also be competition for Michu's signature from Spanish champions Atletico Madrid, Arsenal, West Ham, Southampton and Crystal Palace.