Spanish paper Marca claims Pepe will leave Real Madrid as a free agent to sign for Inter next season.
The 34-year-old defender is running down his current contract and had been expected to go abroad.
Paris Saint-Germain and Chinese Super League club Hebei China Fortune were the most likely options.
However, today’s edition of Marca suggests Portugal international Pepe is heading to San Siro.
They do not specify whether he’s leaning towards Inter or Milan, as both are seeking reinforcements at the back.
However, Sky Sport Italia are confident it's for the Nerazzurri, as Suning Group owners met with Pepe's agent yesterday.