The Germany attacker joined Liverpool ahead of rival suitors Bayern Munich and Manchester City for a fee rising to £126m.
"Florian's requirement was that everyone be comfortable with the move," he told BILD. "He told us, literally, that he hoped Bayer 04 would also be happy with the result.
"There wasn't a single moment (where we realised he wanted to leave), but rather a development. Our goal was to extend Florian's contract and keep him for at least another year. Gradually, we sensed that he was more interested in making a move.
"Starting in February and March, the discussions focused more on other clubs and other leagues. We always knew what he thought. We knew from the parents who they were talking to. The clubs from abroad also informed us, and they handled the matter in a highly professional and serious manner."
He wanted Liverpool
Rolfes also said, "In May, he told us that he had decided to join Liverpool. I believe he's a very good fit for Liverpool. The club has treated him very seriously. Florian was made to understand that they know exactly why they want him. This approach was a very important aspect of the overall package for him.
"All the clubs that had contacted us in advance were clear about the region in which the transfer would take place. We only negotiated with Liverpool after Florian told us that was his preferred club. It was clear to me from the beginning of the negotiations that it would work out. Of course, everyone is fighting for their position, but it was always respectful.
"The people at both clubs know each other so well that a face-to-face meeting was not necessary. We handled the transaction over the phone, via email, and via video conference."