The Uruguayan wide man has reportedly grown unhappy at his lack of playing opportunities, and the Greek giants are ready to offer him an escape route from the Estadio do Dragao
The Uruguay international has been strongly linked with a move away from Portugal after becoming a bit-part player over the last two seasons.
Panathinaikos coach Jesualdo Ferreira is an admirer of Rodriguez after coaching the 26-year-old during his time at the Estadio do Dragao, and it is believed he wants to take the player to Athens.
Portuguese sources suggest that Porto are willing to accept just €3 million for the Uruguayan, whose contract runs out at the end of the season.
Rodriguez, who joined his current club from Paris Saint-Germain in 2008, has made five appearances so far this season.