Ten Hag will be in attendance for United's final match of the season at Crystal Palace on Sunday and is expected to be in Manchester on Monday.
Rangnick will manage United for the last time at Selhurst Park and has already been in dialogue with his replacement.
"We've been in contact via WhatsApp and hopefully we will have the opportunity to meet and speak in person, either at the weekend or Monday morning at the latest," Rangnick said. "I'm looking forward to speaking to him in person and getting to know him in person."
Rangnick and Ten Hag discussed the nuances of the former's consultancy role when the Austrian steps down as United manager. Rangnick, who will start work as Austria national coach next week, has a two-year deal to advise United on their recruitment strategy as they prepare for another squad rebuild.
"We spoke about that in detail," Rangnick added, "about all the different areas where I could maybe be of help. It's not that easy or not that difficult to know in which areas this could be.
"I think we showed that in the last 15 years with Hoffenheim, Salzburg and Leipzig, even for clubs not as prominent as Manchester United, it's possible to identify, develop and even at one stage sell. I know Manchester United is not a selling club but rather a developing and buying club, but this is possible and this is what is most important, that the club finds players for whom it is the next next logical step is in their career, to develop their sporting career.
"If that happens, I can be positive and I can hopefully be encouraging for our fans that we will bring United back to the top."
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