Radradra, who starred for Fiji at the Rugby World Cup in Japan, is homesick in France and wants to return to the NRL, according to The Daily Telegraph.
France's cold weather and family reasons are cited as other reasons for the 27-year-old's willingness to take a major pay cut in order to switch codes once again.
Radradra scored 82 tries in 94 matches for Parramatta between 2013 and 2017, before joining Toulon in 2017.
Last year, he signed for Bordeaux.
The Fiji union international has been linked with the Canterbury-Bankstown Bulldogs and his former club the Eels, but reportedly prefers a move to the Rabbitohs.
"Apparently Souths are looking at every player, but first we've got to sort out what the go is with Sam (Burgess)," Souths hooker Damien Cook told Sporting News.
"But Semi Radradra is a quality player and he did a great job when he was in the NRL. He'd be a great asset to most clubs.
"Who knows? We will see how it plays out."
Radradra made history at the Rugby World Cup in Japan, becoming the first Tier 2 player to be involved in five tries in a single World Cup match in Fiji's 45-10 win over Georgia.
He has scored five tries in 10 international Tests since making his Fiji debut last year.