The Reds were caught illegally 'tapping up' the Dutchman and forced to apologise publicly for their actions.
However, the saga was reignited recently after van Dijk told the club he wanted to be sold this summer. His comments have forced him to train away from his teammates, according to Saints boss Mauricio Pellegrino.
The 25-year old still has five years to run on his contract, but it is expected Southampton will sell him.
Van Dijk will not travel with Southampton when they fly to France next week.