The 20-year-old Englishman has been the subject of transfer interest from a host of Premier League clubs in the ongoing window and the Eagles are claimed to be leading the chase.
Roy Hodgson’s side have made a formal offer of £19m, which could rise up to £25m after add-ons, in an attempt to land Brewster from Liverpool.
The offer includes an option for Liverpool to re-sign the highly-rated striker for a fee of £37m in the future, while also giving the Reds the right of first refusal.
Liverpool are said to be willing to part ways with the 20-year-old centre-forward as they look to raise funds to balance the books, having signed Thiago Alcantara and Diogo Jota for a combined £70m last week.
However, it remains to be seen if Crystal Palace’s offer will be enough to turn the Merseyside-based club’s head.
Brewster has a number of clubs keen on securing his signature before the transfer window closes in early October.
Sheffield United, Newcastle and Brighton are all admirers of the 20-year-old hitman.