The Netherlands international is widely expected to leave the Magpies this summer following their relegation to the Championship and has been strongly linked with a move to Rome.
Despite his team's struggles during the 2015-16 campaign, Wijnaldum netted 11 Premier League goals and it is understood that he is not short of interest from across Europe.
According to Gazzetta dello Sport, Roma will soon open negotiations for the 25-year-old as they look to replace Miralem Pjanic, who has already made the move to Juventus.
Roma are also said to be close to signing Real Madrid midfielder Mateo Kovacic on loan.