The 20-year-old impressed during a loan spell at Swansea City in the second half of last season, finding the back of the net on 11 occasions in 22 appearances for the Championship club.
Liverpool have allegedly agreed to allow the youngster to leave Anfield this summer providing that a buy-back clause is inserted into a deal.
A number of clubs, including Sheffield United, have been credited with an interest in the striker, but according to the Daily Mail, Palace have emerged as the favourites to sign him.
Brewster was involved in Liverpool's preparations for the 2020-21 campaign and also appeared as a substitute in the Community Shield against Arsenal at the end of last month.
The England Under-21 international has not made the squad for either of his side's Premier League games this term, though, and looks set to move on before the October 5 deadline. body check tags ::