The 26-year-old, who was reportedly a Chelsea transfer target earlier this summer, only made his loan move to Elland Road a permanent one at the beginning of July in a deal worth £3.5million.
However, the switch was agreed with Torino in February after he impressed following on from his arrival in England.
Southampton showed an interest in the Swedish centre-back in April but a move never materialised with the club looking at alternatives.
And the player used his social media account to seemingly confirm that he would be staying with Leeds next season:
“It has been the most eventful season during my career and I have everyone around Leeds United Football Club to thank for that,” said the Swede. “See you next season.”
However, things move quickly in the world of football and Football Whispers understands the Saints are revisiting their interest as they look to bring in defensive reinforcements with Virgil van Dijk's future still uncertain.
Jansson has similarities to his Southampton counterpart with both operating on the left side of the defence and both being dominant in the air.
Southampton's interest in Jansson will no doubt give encouragement to Liverpool who are long-term admirers of Dutch centre-back van Dijk.
The 26-year-old former Celtic defender is set for showdown talks with the club this week as he looks to push through a move.
The Dutchman was left out of Saints' pre-season trip to France last week after informing manager Mauricio Pellegrino of his desire to join the Reds.
Leeds won't want to part with Jansson meaning he won't come cheaply but if Southampton do cash in on van Dijk they will be armed with the best part of £60million and Leeds would comfortably make a profit on their centre-back.