The 27-year-old joined the Saints from his boyhood club for £8m in 2015 but is now understood to be nearing a return, despite having come in as a highly rated player when he made the switch to England three years ago.
Clasie struggled to adapt to life in the country and could not reproduce the sort of performances that prompted the Saints to make a move for him in the first place. He would eventually fall down the pecking order at the club.
He spent last season on loan in Belgium with Club Brugge, and despite giving a good account of himself in the Jupiler League, Southampton aren't thought to be ready to take him back.
According to Voetball International, the player is keen on returning from whence he came and it is expected that a deal will be ironed out ahead of next season.
The Dutchman is still very popular among the Feyenoord support, who would likely welcome him back with open arms.
With Karim El-Ahmadi nearing a move to Saudi side Al-Ittihad, it is believed that Clasie will step in as a replacement for the former Aston Villa midfielder, who was instrumental as Feyenoord won the Eredivisie title last year.
Since moving to Southampton, Clasie has only managed 40 appearances for the side.