Coutinho has been superb for Rodgers' in-form team in recent weeks, putting in a virtuoso display in their 5-1 destruction of this weekend's opponents in the Premier League last Saturday before scoring a vital equaliser in the 3-2 win at Fulham on Wednesday.
The 21-year-old has become a key member of the Liverpool first XI since his switch from Inter in January 2013, establishing himself as one of the leading playmakers in the English top flight.
Rodgers paid just £8.5 million to recruit the Brazilian from Serie A - a fee he believes represents a "snip".
"He's an absolutely wonderful talent," said the former Swansea City boss.
"There are very few players at this level now that penetrate with a pass, that play through teams, and he puts teams on the back foot all the time.
"He doesn't always get there. But the quality of his passing and the weight of his passes is sensational, and he's a good guy as well.
"His talent is remarkable. Every single day he does something that makes me think 'Wow, what a talent'."
Despite his form at club level, Coutinho still only has one senior international cap to his name and failed to make Brazil's squad for the friendly against South Africa next month - coach Luiz Felipe Scolari's final selection before naming his preliminary squad for the FIFA World Cup.
However, Rodgers is in no doubt that his player could light up the 2014 showpiece in his home country.
"Brazil have so many good players, but for me he should be in the squad," added the Northern Irishman.
"I don't believe it bothers him so much because he's still very young. I'm sure every Brazilian player would love the opportunity to play in a home World Cup.
"It's not down to him, but I think you'll see him fight even harder to get in there."
