Van de Beek played no part in Eredivisie giants Ajax's 2-1 win over Eintracht after United reportedly emerged as favorites to sign the star midfielder.
The 23-year-old Netherlands international has also been linked with LaLiga duo Barca and Real Madrid, as well as Premier League side Tottenham.
Pre-game, Ten Hag told Ziggo Sport: "There are indeed developments that keep him out of the selection.
"We will see what happens. We'll make an announcement as soon as there's some clarity."
Academy product Van de Beek has spent five seasons in Ajax's first team, accruing close to 200 appearances in all competitions for the Amsterdam outfit.
Following Ajax's victory against Bundesliga opponents Eintracht, Ten Hag added: "The fact that Donny did not play does indicate a direction.
"The request not to let him play did not come specifically from one side. We do that together.
"Agreements have been made about a possible transfer, and if that possibility arises, you must also co-operate."