The Reds' starting line-up for the third-round tie at MK Dons is expected to feature a considerable number of changes from Sunday's 2-1 Premier League win at Chelsea.
And there could be a long-awaited bow for Brewster, the 19-year-old who in 2017 helped England win an Under-17s World Cup at which he was the top-scorer with eight goals.
He was an unused substitute at Stamford Bridge, and Lijnders said of the England Under-21 international on Tuesday: "I was his coach when he came from Chelsea (as a 15-year-old).
"That he is already on the bench away at Chelsea, for me, is massive. It makes us all proud. If he does start or doesn't start tomorrow, he is a player who is every time more ready.
"He had a long injury (Brewster had ankle and knee surgery in 2017-18), it was not that easy for him. But he has goals in him, he has technique, good physically.
"He is a complete striker, a typical nine who can come first post, score with his head, turn in the box, play one-on-one, can score a scruffy goal as well, unbelievable shot. And a good boy. But let's see."
Other youngsters who could be given debuts by Liverpool boss Jurgen Klopp on Wednesday are 20-year-old goalkeeper Caoimhin Kelleher, and Harvey Elliott, the 16-year-old midfielder signed from Fulham over the summer who last season became the Premier League's youngest-ever player.
Winger Xherdan Shaqiri has been ruled out by a small tear in his calf, but midfielder Naby Keita, who has been sidelined for seven games by a groin issue, is fit to make his return to action, while Sadio Mane (knock), Divock Origi (ankle) and Alisson Becker (calf) are unavailable.
Lijnders stressed – with regard to the line-up against the League One Dons – that "we will put a team in place that for me is a Premier League team".
And he said: "We want to compete in each competition, attack each competition. We work so hard to be in this situation where we can compete in each one.
"For me, cup competitions are the soul of football because it represents a past like where smaller clubs can play against Premier League clubs as an example, and give historic games to fans.
"For me, the cup competitions is something special."
The Dutchman was also asked about Klopp claiming the men's coach award, Alisson taking the men's goalkeeper award and the Champions League winners' defender Virgil Van Dijk finishing second among the nominees for the men's player award at The Best FIFA Football awards on Monday.
Lijnders said: "Big compliment for our structure I think. For our owners, for our team, and then of course a big compliment for Jurgen himself.
"I'm really proud. He is not only the face of the team, of course, he is the face of the club and I think not many foreign managers in a different country made the impact he made at Liverpool."
Meanwhile, Liverpool's kit supplier New Balance has started legal proceedings against the club amid reports linking the Reds with Nike.
The Merseysiders' current contract with New Balance comes to an end next summer and reports have suggested the club have been nearing agreement with Nike over a big-money deal.
A Liverpool spokesperson said on Tuesday: "We can confirm that our kit supplier, New Balance, has commenced a legal dispute against the club. We will not be making any further comment during these legal proceedings."
According to The Athletic, New Balance's contract with Liverpool includes a 'matching clause' and the sportswear brand is insisting it has triggered its right to match Nike's offer and should therefore be granted an extension, with Liverpool saying that is not the case.
The PA news agency has contacted New Balance for comment.