Gallagher has been in outstanding form for the Baggies ever since joining on a season-long loan from Chelsea.
And on Saturday, the 20-year-old scored his first goal for the club to see Bilic’s side secure a crucial victory against Sheffield United – their first league win of the campaign.
Having come through the youth ranks at Chelsea, Gallagher has drawn comparisons to Frank Lampard – the player who was his hero as a youngster.
Bilic played alongside Lampard at West Ham. He has also worked with a host of other stars in his glittering career as both a player and manager. And while he doesn’t normally like putting extra pressure on young players, Bilic can understand why Gallagher has been compared to Lampard.
“It isn’t going to help the boy to have so much praise and I’m not a big fan of that but you can’t help but notice it,” Bilic said on the comparison.
“He ticks those boxes. He plays in the same position, he has everything, and it’s not a little bit of everything, it’s a lot of everything.
“The only thing that concerns me, but only in theory, is whether he’s going to be able to maintain this level of concentration and commitment when the praise starts to come to him, but he looks like he is.
“He’s going to need the help of his family and his coaches and his managers, team-mates and entourage but the boy has everything on a big scale. He’s going to be big.”
Gallagher impressed on loan in the Championship last season with both Charlton and Swansea.
But while Bilic was desperate to sign him, he admits he has been surprised at just how well he has adapted to life in the Premier League.
“I wanted him, I knew him from last season, Charlton and Swansea and I did my homework through Frank Lampard and a number of other people,” Bilic continued.
“But despite that I am surprised by what I’ve seen.
“For a 20-year-old guy, I expected him to be full of energy, enthusiasm and motivation for the Premier League.
“I knew it would be like that but for a 20-year-old guy to be that reliable and have the game management to make proper decisions and to basically be so consistent is not normal.
“Twenty-year-old guys have ups and downs. They have flair and quality, they can score a free-kick or do a dribble but then they are gone for a couple of games or four 10 minutes, they don’t like to do the dirty work.
“But that is other people. He is doing all the dirty work and managing the game but then he’s got quality in his locker as well and that, for a young boy, is not usual. I’ve seen it before with great players and he reminds me of them. So much quality but so mature at such a young age. You can see big things in him.”