The Sharks are understood to be interested in securing the services of Springbok flyhalf Handre Pollard.
According to Sunday newspaper Rapport, the 27-year-old World Cup winner's current contract with Montpellier will run out at the end of the current French Top 14 season.
The article quotes an informant as saying that the Sharks have "tried hard" to lure Pollard to Durban, but a more likely destination appears to be an unconfirmed club in Japan.
Montpellier have already signed 21-year-old Italian playmaker Paolo Garbisi, who is believed to be the future of the club.
If Pollard did make the move to the Sharks, he would be the latest star signing at the franchise after their big-money investment from American company MVM Holdings.
He does have experience in Japan, though, where he has previously turned out for NTT Docomo Red Hurricanes and Japanese clubs continue to be a popular option for many international players.
The Springboks currently have Elton Jantjies (Red Hurricanes), Malcolm Marx (Kubota Spears), Kwagga Smith (Yamaha Jubilo), Franco Mostert (Honda Heat), Jesse Kriel (Canon Eagles) and Willie le Roux (Toyota Verblitz) all signed to Japanese clubs, while Pieter-Steph du Toit is also set to join Toyota Verblitz.