Rangnick has signed a six-month contract to serve as interim manager, before taking on a two-year consultancy role at the club at the end of the season.
United will in the meantime continue the process searching for Solskjaer's permanent successor, with Mauricio Pochettino and Erik ten Hag understood to be among the candidates.
When asked what his consultancy role will entail, Rangnick revealed that he had spoken with a number of club figures in recent weeks, including the departed Solskjaer.
"We haven’t spoken about [the consultancy role] in detail in all the conversations we had with John [Murtough, football director] and also with Ed [Woodward] but especially with John.
"I also had a long phone call with [co-chairman] Joel Glazer for more than half an hour. I also spoke with Ole last Sunday before the Chelsea game for almost two hours.
"He was very generous to spend one and a half hours on the phone with me telling me his insight and details about the team.
"But as I said, with all those people we haven’t spoken about what will happen in the next two years from next summer until summer 2024.
"We only spoke about the current situation and how we can find a way to work together."
Rangnick could neither confirm nor deny that the two-year consultancy role would tie him down exclusively to United and prevent him from working for other clubs.
"Again, we haven't spoken about that," he said. "The club told me that they would want to work with me, not only in the short term but also in at least medium team.
"They also want to benefit from my experience and expertise and this would be a question you would have to ask to the board members.
"But, for me, I think it was in the first instance, as I said, I could not turn down this this proposal for the next six and a half months and including then the following two years. I think it was a perfect thing for me to do."
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