The striker joined Sheffield United on a permanent transfer this summer after struggling for game time with the Reds.
He impressed during a loan spell at Swansea City in the second half of last season.
Klopp spoke about the reasons for the club deciding to cash in on the 20-year-old.
"Our guy, our man - this will always be the case in our hearts. But now on the pitch he is Sheffield United. And anyone who knows Rhian will be aware that sentiment will be firmly left outside of Anfield when he arrives today.
"It would not be possible for me to understate my love, respect and admiration for Rhi.
"Such a special guy on and off the pitch. I'm not going to lie, agreeing to that transfer was really hard.
"He is a natural-born goalscorer. It's in his DNA. He is a coach's dream as he is so eager to learn but also a beacon of positive energy.
"He had some really hard moments with us, but throughout he never once lost belief and he was always someone who would light up a room, even when he experienced really tough times.
"We miss him but we are delighted that he has found a fantastic home at Sheffield United.
"Hopefully he has an off-night this evening and then when we travel to Sheffield. But for the other games we all support him and wish him success."