"I think these will be De Ligt's final games with Ajax, but I hope he goes out on a high," Van der Sar told Sky Sport Italia.
"He's been here since he was a child and will end up at a big club."
On De Ligt – who scored the opening goal on the night in Amsterdam midweek before Lucas Moura's hat-trick sent Ajax packing – Van der Sar added: "I think he'll go to England or Spain."
The future of head coach Erik ten Hag has also been discussed amid reported interest from German champions Bayern Munich.
With the club's stunning run to the Champions League semi-final and a chance of winning the league still on the cards, the 49-year-old is likely to draw other looks as well as his star continues to rise.
But Van der Sar says the club have no intention of letting their manager leave this summer.
Asked about Ten Hag, Van der Sar said: "We intend to keep hold of Ten Hag, that is our intention.
"We know there will be a lot of changes within the squad, but we'd at least like to confirm the coaching staff."
Ten Hag's biggest challenge may be getting the club ready for action on Sunday following Wednesday's heartbreak, with Ajax facing Utrecht in a crunch league clash.
The club will close their season against De Graafschap next Wednesday and are currently level at the top of the league with rivals PSV.