Van de Beek spent the end of the season on loan at Everton, and scored in the Toffees' final-day game at Arsenal, but is due back at Carrington for pre-season training next month.
The midfielder was a key part of Ten Hag's Ajax side that reached the 2018/19 Champions League semi-finals before switching to the Reds in 2020.
The Netherlands international will be keen to show what he can do next term after injury affected his impact on Merseyside.
When asked at his press conference if he was keen to see his fellow countryman again, Ten Hag replied: "Yes, of course, we had a fantastic squad in that time in Ajax.