The 22-year-old signed a long-term deal at the Merseyside outfit on Friday, with the Reds reported to have paid £15m to prise the Wales international away from the Welsh club.
Allen scored four goals in 36 appearances for the Swans last season as the midfielder impressed for Rodgers’ side in their first Premier League campaign.
“I have a lot of faith that Brendan Rodgers can bring success, that’s one of the reasons I’m here,” Allen said.
“I wanted to be part of this project, his project, and I’ve really got a good feeling – as I’m sure all the players here have – that this football club is going to go from strength to strength in the next couple of seasons.
“Brendan is so passionate about his football. He works day in, day out to improve the team and everyone individually. Everyone wants to work alongside someone who has that way about them.
“One of his best things is his man management, it’s second to none. He commands the respect of everyone and it’s no different for me.
“To join back up with him was definitely a big pull for me.”
Allen also revealed his delight at getting the chance to play alongside the likes of Steven Gerrard and Lucas Leiva, and the former Swansea star is looking forward to proving himself at Liverpool.
“It’s hard to believe,” he added. “You find yourself pinching yourself. “These are the kind of players I’ve grown up watching and trying to emulate.
“To get the chance to be playing alongside them is a fantastic feeling and it’s only going to enhance my game.
“It’s an opportunity for me personally. I’ve always been ambitious and wanted to play at the highest level I possibly could. When you see an opportunity like this it’s almost impossible to turn it down.
“I’m someone who wants to be the best I can be. Every day, in training or in matches, I always want to improve. You’ll always get 100 per cent out of me and I’m really looking forward to gelling with the top-class players who are here and doing my bit for the club.”
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