The 25-year-old right back has impressed since joining Salzburg in 2015, and offers good versatility down the right side of the pitch.
According to reports within Italy, talks between the two clubs are at an advanced stage, though the Austrian club are said to be holding out for their asking price of €10m.
It is understood that Lainer would come into the Naples side as a backup for the highly-rated Elseid Hysaj, the club's regular right back.
Albanian international Hysaj is also a player understood to be wanted by a number of clubs this summer, including a possible reunion with former manager Maurizio Sarri should the Italian join Chelsea.
Nevertheless, even should Hysaj remain, Lainer has produced impressive statistics this season to merit his move to Serie A and the opportunity to grace Italian football's top flight.
The Salzburg-born player has made a total of 55 appearances for his club this season in all competitions, including helping his side retain their domestic title and reach the semi finals of the Europa League.
He scored twice and produced 11 assists in all competitions too this season for Salzburg. One of those goals came against Serie A opposition too, when Lainer netted in a stunning 4-1 win over Lazio in the Europa League quarter finals.
Lainer has five senior international caps for Austria, having made his debut in March 2017. A product of Salzburg's academy, Lainer has won three domestic titles and two domestic cups in the last three years since returning to his original club. He spent a season with SV Reid during his time away from Salzburg.