Real Madrid are aiming to complete the signing of Trent Alexander-Arnold before the start of the Club World Cup.
The England defender has confirmed he will leave Liverpool when his contract expires this summer and the 26-year-old is expected to join the Spanish club as a free agent.
Alexander-Arnold's contract with Liverpool expires on 30 June but the Club World Cup begins 16 days earlier.
BBC Sport understands Real have approached Liverpool with a view to negotiating a deal to release Alexander-Arnold in time for the full-back to be part of their plans for the Fifa-organised tournament in the United States.
It is understood the Spanish club are considering an offer of about £850,000 to release Alexander-Arnold early from his deal.
It has also been suggested Real might be willing to pay the wages Liverpool owe Alexander-Arnold as they seek a solution.
Discussions between all parties are described as amicable.
World football governing body Fifa has confirmed there will be a short initial transfer window this summer - running from 1 to 10 June - which is designed for clubs competing in the Club World Cup to amend their squads in time for the competition.
Real's desire to land Alexander-Arnold in time for the tournament presents an opportunity for Liverpool to recoup at least some money for a high-value player who will otherwise leave Anfield for no fee.