The England under-21 star hoped to break into Jurgen Klopp’s first-team this season after impressing on loan with Championship outfit Swansea City last term.
Swansea are believed to be keen on having Brewster back at the Liberty Stadium – but Premier League side Palace have now joined the race to sign the 20-year-old.
The Reds are keen to bring some funds in, with Diogo Jota and Thiago Alcantara signing for almost £70million last week.
The south Londoners are locked in talks with Klopp’s men, hoping to finalise a bid that will reach £20m with extras.
It is understood that the Reds are demading a buy-back clause is inserted in any deal and while Palace are not prepared to do that, they will include a hefty sell-on fee to try and seal the deal.
Brewster is said to be prioritising first-team football, with Palace offering him the clearest route into regular Premier League minutes.
Klopp’s assistant Pep Ljinders added further fuel to the fire this week, when he refused to rule out a move for the former Chelsea youngster.
When asked to address Brewster’s future, Ljinders said: “These things have to be discussed in the boardroom, we cannot discuss transfer policies here with the press before the deadline.”
Liverpool have been extensively linked with Watford ’s Ismaila Sarr, with the financial boost Brewster could provide going a long way to signing him.
However, their interest is now believed to have cooled having signed Jota from Wolves for a fee that could reach £45m.
Get the latest Liverpool transfer news straight into your inbox, click here.