The 19-year-old has made just one appearance for the Reds this season.
And Brewster revealed he asked to leave the club temporarily in the summer.
"He said no straight away, so that shows that he has great faith in me and wants to push me towards the first team," Brewster said.
"Obviously it's hard, with our front three, to get game-time because they're all amazing players. It's going to be difficult, but you just have to keep going and going."