Leeds and Swansea - whose manager Steve Cooper managed Brewster at international level - had already been credited with interest in the Liverpool striker, alongside Premier League clubs.
It comes less than a week after the Crystal Palace manager, Roy Hodgson, admitted he cannot offer Brewster the regular game time likely to be sought by Liverpool should the Reds grant a January move.
And England's second tier is becoming an increasingly plausible destination if so - although Leeds' failure to provide their on-loan Arsenal striker, Eddie Nketiah, with frequent minutes in the first half of the campaign may harm their chances of a deal.
Liverpool will make a definitive decision over Brewster's future after the their FA Cup third-round tie with Everton, in which the Londoner could be involved, according to The Times.
Liverpool fans - which of Leeds, Swansea, Blackburn or Wigan would you rather Brewster was loaned to?
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