The 26-year-old playmaker has penned a long-term deal with the Reds after Liverpool agreed a £23m deal with Southampton for the England international.
Liverpool are buying themselves a tremendously gifted forward player who, for me, is going to enhance the team
Lallana, who helped the Saints secure back-to-back promotions to the Premier League, scored nine goals and made six assists in 38 top-flight appearances last season.
And Case, who won five top-flight titles and three European Cup with the Merseyside club, believes England midfielder Lallana is a Brendan Rodgers player.
“I’m more than pleased Liverpool have bought him,” Case told the Liverpool Echo.
“To be honest, I have always had a suspicion they may make a move for Lallana. He is a Brendan Rodgers type of player. I was speaking to people around Southampton a few years ago and even then I was saying it was a wonder nobody had come in to take Lallana when the club were in a lower division.
“Rickie Lambert was playing alongside him then, too.
“Lallana has always been a gifted boy. When he came from Bournemouth, even then there was a buzz about him. You knew he was a good player. I thought he would have left Southampton years ago. He has been their best player for a long, long time.
“He can play anywhere. Lallana is such a versatile player. Some of the skills he has on the ball, the way he receives it and controls it, are a real joy to watch.
“His creativity is excellent, but it is always within the framework of the team. He works hard and doesn’t shirk responsibility. Liverpool are buying themselves a tremendously gifted forward player who, for me, is going to enhance the team.”
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