Rodgers was part of Scolari's coaching staff at Chelsea and the Northern Irishman has been asked to do some unofficial scouting for his former colleague.
Midfielder Coutinho has been capped just once at senior international level, but, having watched the 21-year-old at close quarters this season, Rodgers believes that he has plenty to offer the World Cup hosts.
"I am constantly on to Scolari about him," Rodgers told reporters.
"Felipe has just asked me to keep an eye on the Brazilian boys – even ones at other clubs [in England] – but I'm only concerned about the ones here."
Coutinho has scored four goals in 23 Premier League appearances since moving to Anfield from Inter Milan in January.