The 20-year-old was on loan with Swansea City in the second half of last term.
He managed 11 goals in 22 games for the Swans in the Championship.
It appears the Reds want both a sell on clause and a buy-back agreement within the deal.
Liverpool could decide to buy-back Brewster for a fee that is agreed on - or benefit from a percentage of whatever Palace get from selling him on in the future.
Brewster has also been strongly linked with Sheffield United in recent weeks.