According to 'Sky Sports Italia', the Colombian international will undergo a medical on Thursday to join Carlo Ancelotti's side.
'I Ciucciarelli' are in the market for a new goalkeeper due to the injury of new signing Alex Meret. The Italian broke his arm in a training session last month.
If Ospina impresses during his reported season-long loan spell, Napoli will have the chance to sign the 29-year-old on a permanent deal.
Ospina featured as Colombia's No. 1 for their four World Cup games this summer until 'La Tricolor' bowed out on penalties to England.