The arrival of Julio Cesar has been rumoured by Gianluca Di Marzio, who works for Sky Sports in Italy, while it was also tweeted by CNN Italian correspondent Tancredi Palmeri.
The goalkeeper was a member of the Brazilian side which beat Spain 3-0 in the Confederations Cup final late last month, conceding just three goals in the whole tournament and playing in every game for Phil Scolari's side.
QPR were relegated from the Premier League last season and will be looking to get Cesar off their already large wage bill following the drop to the second tier of English football.
Napoli, meanwhile, are looking to build under new manager Rafael Benitez, who looks set to lose the prolific Uruguayan striker Edinson Cavani, per SkySports.
This could be one of many signings for Napoli with Real Madrid's Jose Callejon on the brink of joining the Rafa revolution at the Naples club.
Cesar has made a total 74 appearances for the Brazil national team and has played under the Spaniard during his infamous short spell at Inter, where they won the FIFA Club World Cup.
The 33-year-old had been linked to Premier League side Arsenal with their goalkeeping situation not looking particularly solid, per Sami Mokbel of The Daily Mail, but they look to have missed out on his signature.
Cesar would leave a question mark on the future of Italian International Morgan De Sanctis who has made 155 appearances for the club since he joined them from Galatasaray in 2009. He has six national caps to his name, but is coming to the end of his career at the age of 36.