The Brazilian playmaker has earned a legion of admirers on Merseyside following his £12 million move from January 2013 and the creative Coutinho played a large part of the Reds' title challenge last season.
The former Inter youngster made 33 appearances last term, scoring five goals and seven assists as the Reds mounted their closest title challenge for 24 years.
The loss of Luis Suarez to Barcelona has only increased the responsibility on the shoulders of Coutinho in the new season, but the 22-year-old will be aided by the likes of Lazar Markovic and Adam Lallana, who were signed earlier the summer for respective fees of £20 and £25 million.
And speaking to the club's official TV station, McDermott, who played for the club from 1974-1982 and won three European Cups and five league titles during his time at Anfield, has backed Coutinho to thrive.
The ex-midfielder thinks that Coutinho has the ability to develop into a world-class talent under manager Brendan Rodgers.
McDermott said: “There’s no doubt about it, he’ll be a world star. He’s 22, that’s no age at all. He’s got everything. He go past players but I’d like him to score a few more this season because he’s capable. He showed that with the winning goal against Manchester City.
“He’s going to play a big part in what happens this season, because if we can get him playing well, with one or two others, we’ve got a great chance of having a good season."
McDermott also explained how Daniel Sturridge will have a "big pressure" placed on him in the absence of Suarez but feels that the Reds star's relaxed nature hints at a player who is unfazed by the expectation.
“It’s a big pressure for him, when I’ve seen him on television, he’s a bright spark, always joking around and he’s confident in his own ability," he added.
"It’s a big season for him and if he can get another 20 goals this season then the problem we’ve got is, how are we going to make up for the 31 goals [scored by Luis Suarez last season], and I think they’ve got the players to do that."
Meanwhile the 62-year-old former Newcastle United coach challenged Jordan Henderson to add more goals to his game, after netting just four times last term.
“I think he’s got to look between 12 and 15 because he’s capable," he said. "He gets forward and he’s got a great engine. He’s still learning and I’m sure he’ll admit that , but if he can chip with 12 or 15 goals a season, then it’ll compensate for losing Suarez."