The 20-year-old midfielder has already worked with Ronald Koeman during their time at the Eredivisie club before his move to the Premier League.
Cork will be able to leave on a free transfer if he decides not to extend his current deal so the Saints may be forced to sell him before the end of the January window in order to avoid letting him go for nothing.
Vilhena played his way through his current side’s youth academy and impressed during his time working with Koeman.
However, he has been unable to replicate his previous form under new manager Fred Rutten with the Netherlands Under-21 ace now tipped to be given the chance to be reunited with his former boss.
He has only started eight matches from a possible 19 this season and is yet to score a single goal, compared with last season where he started 29 games and scored six.