The 22-year-old Brazilian has made a big impression in preseason and his manager expects big things from the former Inter midfielder both at home and in Europe.
The Brazilian playmaker has regularly shown glimpses of his ability since arriving at Anfield from Inter in January 2013.
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He made 33 Premier League appearances as Liverpool went agonizingly close to winning the title last season and was one of its standout players throughout preseason after missing out on a place in his country's World Cup squad.
The Reds will return to the Champions League in 2014-15 following a five-year absence and, after watching a virtuoso Coutinho display in his side's 4-0 demolition of Borussia Dortmund on Sunday, Rodgers tipped the 22-year-old to shine on European club football's biggest stage.
"He's so gifted - his ability is magical [and] the weight of his pass is phenomenal," Rodgers told reporters. "He's come into the country and lit it up with his quality. [The important thing for his development] is sustaining that level of performance.
"He's got the opportunity to show he's a top-level player in the Champions League and he'll do that. Over the next four or five years, he'll be a big talent in world football for Brazil and Liverpool. We're lucky to have him."
Coutinho - whom the manager hopes to tie down to a new contract - was among the scorers as Liverpool routed Dortmund at Anfield and Rodgers was thrilled with his team's performance.
"[I'm] delighted with the result - they [Dortmund] have been one of Europe's best teams for the last three or four years," he added. "We were excellent and this brings to an end what has been a very good pre-season."