The 29-year-old is currently sidelined following knee surgery and likely won’t return to action before November.
The report suggests the Partenopei have already opened taks with Inter regarding a loan deal with an option to buy.
At this time Napoli want that option to stand at €12 million, however the Nerazzurri are looking for a figure closer to €18m.
Inter are keen to offload players from what is a packed midfield after the arrival of Arturo Vidal from Barcelona, with Vecino joining the likes of Joao Mario and Radja Nainggolan as potential departures.
Last season Vecino netted three goals in 25 appearances in all competitions for Inter.