Ten Hag is taking over from Rangnick as permanent boss after the Red Devils' final Premier League game of the season against Crystal Palace on Sunday.
However, the former Ajax boss has already travelled to the UK to begin work as early as possible, and he will be in attendance at Selhurst Park for the Palace game.
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Speaking before the fixture, Rangnick confirmed that although he has not enjoyed face time with Ten Hag yet, he would be meeting his successor soon.
"We have been in contact, via WhatsApp, hopefully we have chance to meet and speak in person at the weekend or Monday morning at latest," he said.
Listen now to 90min's Manchester United podcast, The Promised Land, with Scott Saunders & Rob Blanchette. On this week's show they discuss the latest news surrounding the club including a discussion regarding Ten Hag's arrival and his Ronaldo hint.
Rangnick will take over the Austria national team after the Palace game, and it was planned for him to move into a consultancy role at United as well - though there have been rumblings that the German will ultimately have little influence at the club.
Quizzed about his future, he added: "We spoke about that in detail, how I could be of help. I think we showed at Hoffenheim, Salzburg and Leipzig that is is possible to identify, develop and sell. This is what is most important for whom it is the next logical step in their career."
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