Despite him being out of contract at Anfield last summer, Liverpool did receive a fee of around £10M for Alexander-Arnold as Madrid wanted the defender ready to compete in the FIFA Club World Cup.
Real Madrid manager Jose Mourinho is reportedly still working out whether he will keep the England star who also missed out on this summer’s World Cup side.
The 27-year-old endured a difficult first season in the Spanish capital, with injuries and managerial changes limiting him to just 14 La Liga starts.
Now, Andy Townsend has backed the defender to make his way back to Merseyside in a move that many Liverpool fans would feel concerned about.
"First and foremost, purely as a player, if he came back to Liverpool, would he improve them? One hundred per cent, yes. (Jeremie) Frimpong, as a right back, I’ve not really got. It’s so important nowadays with these full backs being such an important part of a team’s attacking intentions.
"If you can’t deliver anything half decent when you get into a good area, and from what I’ve seen of him so far, I’ve not really seen that final delivery, which Trent can do in his sleep.
"So, I think he absolutely would improve them. The question is how the club would feel about it. That’s going to be a difficult pill probably for some Liverpool fans to swallow.
"Real Madrid have signed Denzel Dumfries from Inter, who would no doubt fit the profile a bit more for Jose Mourinho. They’ve got (Federico) Valverde. They’ve got other players. They’ve got plenty of cover in that sort of area. So, if you’re Trent, at this stage of a pre-season, he will want to think he’s got every chance of starting and getting on with it."
New Liverpool boss Andoni Iraola has used Jeremie Frimpong and Calvin Ramsey at right-back so far in pre-season which may not leave room for Alexander-Arnold who could cost upwards of £50M from their European rivals.