Jurgen Klopp has subsequently been left with only two recognised senior centre-backs to choose from, raising the likelihood that they will dip into the transfer market when the window reopens.
Liverpool scouted White intensively during his loan spell at Leeds United last season and considered a move for him in the summer, only to be put off by his asking price.
The Mirror reports that Brighton have now told the Reds that it will take a bid of £50m to prise the 23-year-old away from the Amex Stadium midway through the season.
The Seagulls rejected three bids for White from Leeds during the summer but would not stand in his way if one of the established 'big six' lodged a suitable offer.
The centre-back only signed a new long-term contract at the beginning of last month, keeping him at the club until 2024.