The 20-year-old has enjoyed a successful loan spell at Championship side Swansea City, registering four goals in 11 league fixtures prior to the coronavirus postponement.
Recent reports have suggested that table-toppers Leeds are keen on a deal for Brewster, but Mills believes that the striker would not be guaranteed consistent game time under Marcelo Bielsa.
Speaking to Football Insider, Mills said: "He is not ready to lead the line, that is for sure. You would need somebody with out-and-out experience of the Premier League.
"You might as well stick with Patrick Bamford if you are going to go with Brewster. Undoubtedly he has got talent, but he is unproven.
"If you are going to replace somebody you have to have the guarantee that they are better than what you have got."
Brewster has made three appearances for Jurgen Klopp's side but is yet to debut in the Premier League.