The Merseyside outfit targeted the Guinea international earlier in the summer, but they were knocked back numerous times.
It is believed that Jurgen Klopp's side went as high as £66m in the bidding, but it was to no avail as the Bundesliga club made it clear that the midfielder is not for sale.
"There were two offers from Liverpool and in between times also a telephone call between the clubs," Goal.com quotes Rangnick as saying. "But not between me and Jurgen Klopp.
"For us, it was always clear that we would not give Naby Keita. That is why there was no direct contact. Every club that has sporting ambitions would have done the same as we did.
"But we must weigh it up. If we let Keita go for €70-80m (£63m-£72m) this year, what more would that bring us compared to the sum we would get next year?"
Keita scored eight goals and produced seven assists in the Bundesliga last season.