Marca says Vargas will move to the Mestalla on a season-long loan deal for a fee of €1.5 million (£1.2m).
Should Valencia want to keep Vargas past the end of this summer, reports say a fee of €3m (£2.4m) will be due to Napoli.
Los Che Coach Juan Antonio Pizzi has publically confirmed both his interest in Vargas and his hope the club sign a striker, with the deal expected to be ratified soon.
Vargas moved to Napoli from Universidad de Chile in 2012 but struggled to maintain his place in the side.
The 24-year-old was allowed to join Gremio on loan in January 2013, with the deal coming to an end in December.
It is thought Vargas will be able to make his Valencia debut against Espanyol on Saturday.