Trent Alexander-Arnold pre-match, with Andoni Iraola in a circular inset
Trent Alexander-Arnold pre-match, with Andoni Iraola in a circular inset
The 27-year-old has not had the desire impact at Los Blancos after his highly-publicised move from Liverpool last summer, leading to question marks about his long-term future.
A return to the Premier League with Liverpool had been tipped in recent weeks, while Arsenal are also interested, but both clubs could now be set to miss out.
Former Man United chief scout Mick Brown told Football Insider that Alexander-Arnold is determined to make a success of his "dream move" to Real Madrid
This comes after both the player and the Spanish club worked hard to secure the move on a free transfer, and they are currently unwilling to call time on his spell.
Alexander-Arnold is also expected to have reservations about a return to Liverpool in the near future, given the angry reactions of the supporters when he opted to leave.
Could Trent Alexander-Arnold leave Real Madrid?
Brown told Football Insider in January that Premier League clubs including Man City were plotting moves to bring Alexander-Arnold back to English football.
He has largely struggled to make an impact in Madrid, and so far this season has started just two of a possible seven La Liga games, leading to questions about his future.
However, the England international is working hard to impress Jose Mourinho and believes he can still be a success in Madrid, in a blow to his many potential suitors.
"It would be a huge surprise if Liverpool looked to bring Alexander-Arnold back,," Brown told Football Insider.
"I'm led to believe things haven't quite worked out for him at Real Madrid so far, but he made his bed and now he has to lay in it, I don't think he'll be looking to leave already.
"A lot of work went into the deal to lure him to Real Madrid in the first place, the club pushed really hard for it and he had a big decision to make.
"By all accounts, it was his dream move, so I don't expect him to be willing to call time on that just yet. He's going to be working hard to prove he deserves to be there.
"Alexander-Arnold will be determined to make something of his Real Madrid career, so any suggestions of a move back to Liverpool can be cast aside for now.
"I'm not convinced it would be the best move for him anyway, when you consider how the fans reacted when he left in the first place."
How do Liverpool feel about re-signing Alexander-Arnold?
While it has been made clear that Alexander-Arnold is not currently considering a return to Anfield, the club have been consistently linked with a potential move.
Andoni Iraola is keen to strengthen at right-back, leading to the inevitable suggestions that their former academy product could be on their radar.
However, Brown told Football Insider on 29 September that Liverpool are not currently considering a move for Alexander-Arnold and are prepared to look elsewhere.
The Reds have moved on since his departure, while the England international is believed to be content with life in Madrid, squashing any hints of a return.
Instead, Alexander-Arnold is considered likely to remain in Madrid, with Liverpool not planning to bring him back to English football any time soon.