The Brazilian playmaker has regularly shown glimpses of his ability since arriving at Anfield from Inter in January 2013. He made 33 Premier League appearances as Liverpool went agonisingly close to winning the title last term and was one of their standout players throughout pre-season after missing out on a place in his country's World Cup squad.
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"He's so gifted - his ability is magical [and] the weight of his pass is phenomenal," Rodgers purred to the press.
"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."