The 19-year-old is set to be made available for a loan deal in January by Liverpool manager Jurgen Klopp.
Brewster, highly rated by Klopp, is to be allowed out to get some game time, having made only two Carabao Cup appearances so far this season.
The youngster led the Liverpool attack in their 2-0 win over MK Dons at Stadium MK in September, and then converted a penalty in the shootout victory over Arsenal in the following round back in October.
But so far in the Premier League he has been limited to three appearances on the substitutes’ bench and is still awaiting his first-term bow in the top flight.
Palace have been looking for another striker to back up the misfiring Christian Benteke since the summer.
They failed to get Chelsea striker Olivier Giroud then and have since cooled on the Frenchman, but are still interested in Celtic forward Odsonne Eduard.
But the Frenchman would cost around £20 million and the Scottish club are reluctant to sell their prized asset.
Roy Hodgson’s side have struggled for goals all season, with neither Benteke or Jordan Ayew convincing. They have so far scored only 11 league goals this term, of which Ayew has netted four.
Aston Villa, though, are also ready to make a bid for Brewster.
Brewster revealed last month that he had sat down with Jurgen Klopp to talk about his role in the team.
“Be patient and you’ll play,” said Brewster when asked by Scouted Football what he had been told by Klopp. “Wait for your time and hopefully it’ll come.
“My relationship with him is very, very good. He’s easy to approach and easy to talk to. I think you need a manager like that.
“You can’t think it’s easy and you’re just going to get there with your talent, because you need to work hard as well.
“I’ve seen a lot of people with talent but not everyone makes it because of the attitude and the drive.”
Brewster made Liverpool’s travelling squad for the Champions League final in Madrid in June, when the Reds were allowed to name 12 appearances.
And reflecting on that, combined with his first-team debut in Milton Keynes, he is keen for more game time on Merseyside.
“No doubt making my debut away at MK Dons was amazing, I hope it’s the first of many,” the teenage frontman added.
“The support of the fans was amazing, but being in Madrid was different.”