Real Madrid is supposed to complete a deal to hire Liverpool right -back at a free transfer this summer.
Alexander-Arnold is not a contract at the end of this season and has not agreed to extend it.
As a result, the England star could leave free of charge in summer, and according to several reports, Real Madrid will now tend to sign it.
The 26-year-old was strongly connected to the Spanish giants in the past 18 months.
Alexander-Arnold is one of three Marquee Liverpool players who should not have a contract in the summer.
Mohamed Salah and Virgil van Dijk are in the same boat and both still have to sign new offers for Merseyside.
Salah, who is the best scorer of the Premier League this season, was strongly connected to Saudi Arabia.
The captain of Liverpool, van Dijk, has now been advertised as a reported goal for French champion Paris Saint-Germain.
Alexander-Arnold was associated with a move to Real Madrid during the transfer window in January, when Liverpool could have requested a fee for him.
However, the red showed no interest in it, and manager Arne Slot said at the time that Alexander-Arnold was committed to the association.
“I think everyone saw how great a first half of the season he had, how much he is here, how much he wants to win here,” said Slot.
“I see him on the training area and works every day. He is fully committed to us and will play on Sunday.
“If the players were destabilized in Liverpool, if other people talk about it, we would really have a problem.
“When they play in one of the largest clubs in the world, everyone always speaks about them, sometimes in relation to other clubs. This happens so often for our players.
“There have been some discussions about our players in the past six months, and I don’t think that has destabilized them at all.”