Allen, who joined the Anfield club earlier today for a fee believed to be £15m, revealed that Rodgers was a key factor in his decision to move.
"To join back up with him was definitely a big pull for me. Brendan is so passionate about his football. He works day in, day out to improve the team and everyone individually," Allen told the club's official website.
"Everyone wants to work alongside someone who has that way about them. One of his best things is his man management. He commands the respect of everyone. I have a lot of faith that Brendan can bring success.
"I wanted to be part of this project and I've really got a good feeling this football club is going to go from strength to strength in the next couple of seasons."
Liverpool's first match of the new Premier League season comes against West Bromwich Albion on August 18.