The 20-year-old impressed at Swansea on loan, and is now going to battle for a first team place with Jurgen Klopp's team.
But if he is on the market, Spurs would like to sign him on loan, per Football Insider.
The club want a backup for Harry Kane, and they see Brewster as the ideal option.
It is unclear if the player would want such a move, as he could be a backup at Liverpool as well.
Several Premier League and Championship clubs also want Brewster on loan, per the source.