33-year-old Cavani is a free agent after his Paris Saint-Germain contract expired and a number of clubs have shown interest.
But Benfica have taken the lead in recent weeks and are very close to signing the Uruguyan striker.
According to Gianluca Di Marzio, Cavani is expected in Lisbon on Monday to finalise his move to Benfica.
The Portuguese side are ready to hand him a three-year deal worth a mammoth €10m-per-season.
Benfica completed a triple deal for Everton Soares, Jan Vertonghen and Luca Waldschmidt last week.
A number of other high profile names are linked with the Aguias, but the arrival of Cavani will undoubtedly be their most eye-catching of the summer.