According to The Daily Star, the Dutch manager is looking at Guidetti to replace the departed Ricky Lambert, despite having already signed Italian target man Graziano Pelle.
The 22-year-old spent the 2011/12 season playing under Koeman at Feyenoord, and scored 20 goals in 23 appearances leading the Dutch side to second place in the Eredivisie.
Since that season, Guidetti's career has stalled somewhat. In the 18 months since his phenomenal campaign in Holland the young Swede has struggled with illness and injury.
Stoke City took him on loan in the January transfer window, but he had a troubled time at the North Staffordshire side. He only made six substitute appearances for the Potters and didn't score a single goal.
His Stoke stay would not have been helped by his high-profile falling out with boss, Mark Hughes. Guidetti reportedly slated the Welshman to the Swedish media for not giving him a real chance in his side, but later went on to claim it was his intention to be disrespectful to Hughes.
Southampton will have considerable transfer funds available to them after the sale of Lambert and Adam Lallana to Liverpool and Luke Shaw to Manchester United.
Despite never having made a single league appearance for the Premier League champions, City reportedly value the forward at £6 million.
Should Koeman make a move, Guidetti would become the Saints' third signing of the summer after Dusan Tadic and Pelle, who both joined Southampton from the Eredivisie and cost a combined total of £18 million.