The Germany Under-21 international moved to Anfield in July after just one season at Leverkusen.
Can came through the ranks at Bayern, and made four league appearances before the switch to their Bundesliga rivals.
The midfielder, who has seen his opportunities at Liverpool limited by an ankle injury, revealed he opted for a move to the Premier League instead of returning to Bayern.
"Bayern had a buyback clause but that didn't kick in until next year," he said.
"There were some discussions with Bayern this summer but I decided the best thing for me would be to accept the opportunity to come to Liverpool.
"Before I came here I had discussions with Brendan Rodgers and that made my mind up. From those talks I was very positive about this move.
"This whole club is very ambitious and positive about how it wants to play football. That's the way I want to play football too.
"Liverpool believe in the same things and that's why I came here. I want to stay here for a long time."
