The Reds centre-back says his Netherlands team-mate is making a great step forward in his career by moving to Old Trafford
Goal understands the Red Devils are closing in on a deal for the 23-year-old after agreeing a fee in the region of £40 million ($53m).
The midfielder was left out of the Ajax squad for Saturday’s friendly against Eintracht Frankfurt, fuelling speculation a move to the Premier League was imminent.
Ajax boss Erik ten Hag later confirmed Van de Beek’s future at the club was up in the air and a key reason behind his omission.
Van Dijk knows Van de Beek’s talents well, having played alongside the midfielder for the Dutch national team.
When asked by reporters about Van de Beek’s move to Old Trafford, he gave it his seal of approval, despite the fierce rivalry between United and Liverpool.
He also expressed his delight for fellow international team-mate Nathan Ake, who completed a move to Manchester City earlier this summer.
“From my heart, I wish him the best. It’s wonderful for him, it’s a nice step for him to move to a great club as a Dutch player.
“Also the same for Nathan Ake, who moves to Manchester City. I’m glad for both of them.”
Once the deal is confirmed Van de Beek will become United’s first major signing of the summer, ending weeks of frustration in the transfer market for boss Ole Gunnar Solskjaer.
Dortmund are holding out for a fee of €120m (£108m/$142m) for Sancho, but United believe that is not a realistic figure given the state of their finances due to the impact of Covid-19.