The Nigerian departed after six years at Anfield last week, although he failed to register a single senior appearance for the club.
Reds manager Jurgen Klopp told Awoniyi the fact Union Berlin parted with a club-record transfer fee to acquire him is a good thing because it proves they wanted him.
“He (Klopp) said it was a good thing because he felt like everyone at Union wanted to sign me at the club," he told Kicker. “He said it was the most important thing for a young player."
Before adding: “I am convinced that Union is the best move for me at the moment. Maybe one day I'll go back to England. Who knows."
Speaking on his departure last week, Awoniyi said: “After lots of loan moves in previous years, I want to finally come and have a home.
"I owe so much to Union, so it makes me happy and proud to be back here. It's fantastic to continue on the great path with the club. I will give everything to quickly pick up where I was before my injury."
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