The pair worked together during Rodgers' time in charge at Liverpool, with Coutinho spending two-and-a-half years working under the Northern Irishman.
Speaking following the completion of the Brazilian's move, Rodgers said that he was not surprised by the fee and backed his former charge to step up and shine at the Camp Nou.
"Neymar's move [Barcelona to PSG for £198m] has changed the dynamics and a lot of the South American players have dreams of playing for Real Madrid or Barcelona," he explained.
"He certainly has the quality to play for Barcelona."
Meanwhile, Rodgers also reminisced on how he had to convince the relevant body that Coutinho was worthy of being awarded a work permit when he joined Liverpool as an 18-year-old.
"He only had one Brazil cap when he moved to the country," Rodgers recalled.
"I remember going to Wembley to attend the work permit hearing and trying to convince the panel to allow him in the country to play.
"Barcelona's a good move for him, and for Liverpool it is a huge return on what they paid."