Real Madrid are considering a £20 million bid to persuade Liverpool to sell Trent Alexander-Arnold in January, but the Premier League leaders are adamant their vice-captain will not leave this month.

After an initial approach from Real was firmly rebuffed, the European champions are expected to return to test Liverpool’s resolve. But the Merseyside club says they will not be willing to negotiate a deal even if such an offer materialises.

Liverpool’s position is that whatever fee they might receive for the right-back is secondary to their Premier League title and Champions League ambitions. They are interested in trophies, not what numbers they can secure for a pivotal player.

Indeed, a fee in the region of the €25 million Real Madrid have indicated they would pay could be collected in prize money should Arne Slot lead the club to its second Premier League title in 35 years or win a seventh European Cup.

Liverpool have still not given up hope of convincing their vice-captain to sign a new long-term Anfield contract instead of moving to Real Madrid on a free transfer at the end of this season. In the light of Real’s move, many will believe the likelihood of Alexander-Arnold staying at Anfield is receding.

Real’s effort to try to buy the player early demonstrates their confidence that if they do not sign him this month, they will do so in the summer.

Alexander-Arnold has been involved in lengthy contract talks but as in the case of team-mates Mohamed Salah and Virgil van Dijk, from the outset there was a gap between what the player believes he deserves for stellar service and what the club considers affordable within their budget and successful policy of self-sustainability.

The club hierarchy have never hidden the fact they cannot pay the same wages across the board as clubs like Real Madrid, Manchester United or Manchester City, but they have still given their superstar players contracts worth upwards of £20 million per season.

It is a policy which has already brought huge success to Liverpool as they won every major honour under Jurgen Klopp and would have won more but for City and Real. Liverpool’s owners have taken pride in their ability to regularly go toe-to-toe with those clubs having constructed elite-performing teams with a vastly different approach.

Liverpool have held firm in such contract impasses before. Steven Gerrard was arguably the club’s greatest player and club captain when he was not given the deal to end his career at his boyhood team, joining LA Galaxy in the summer of 2015.

Another legend, Roberto Firmino, moved on two years ago as Liverpool were not prepared to renew on similar terms to that which the Brazilian was earning at his peak. Other key first-teamers such as Emre Can and Georginio Wijnaldum also moved on for free when their salary expectations did not meet the valuations of their club, contract talks ending without agreement.

The contract situations of Alexander-Arnold, Van Dijk and Salah have been the biggest test yet of the Fenway Sports Group’s policy, the situation of the older players significantly different to predecessors because they are playing to such a high level aged 33 and 32, respectively. Calculating their value if they are still at the club aged 35 and 34 is more complicated.

For Alexander-Arnold, being a top earner as a right-back reflects his uniqueness as a footballer. Should he sign for Real Madrid, his salary is likely to be akin to that of a star striker or midfielder.

Should he move to Spain, Alexander-Arnold could bank a considerable signing-on fee on top of his weekly wage because Real will be saving the £20 million they are willing to pay Liverpool this January. Were he still under contract, Liverpool would be valuing Alexander-Arnold at around £100 million, at least.

Will Alexander-Arnold go? Expert opinions:

The optimistic Liverpool fan has always believed that in the cold light of day Alexander-Arnold would consider everything he has at Anfield and commit to his boyhood club for the rest of his career. Real Madrid’s official move has punctured such romanticism. Real Madrid usually get who they want, especially when no transfer fee or club negotiation is required as is the case to sign the defender for free this summer.

Real Madrid will not have made the call to Liverpool without knowing Alexander-Arnold wants to go and that making an offer now would be rejected. It was a smart move. It also means everyone saves face. Liverpool can say they did all they could – and turned down money for a player who can leave for free in the summer – Madrid have shown how much they want him and Alexander-Arnold did not just run down his contract. It is a familiar tactic from Madrid, and other clubs such as Bayern Munich, and usually a successful one.

Alexander-Arnold has made more than 330 senior appearances for his boyhood club. He has won every major trophy in a Liverpool shirt: Premier League, Champions League, Club World Cup, FA Cup and League Cup. He is 26 years old, in his prime as a footballer. There will never be a better time than this summer for him to pursue a new challenge. And there will never be an offer as spectacular and tempting as the one to join Real Madrid as a free agent.

Liverpool supporters will want him to stay as a one-club man but he has already won it all at Anfield. How many worlds are there still to conquer in his home city? Another Premier League and Champions League? He could do that this season and still get the move to Madrid. This is the chance of a lifetime to play for the most glamorous team in world football. Financially and emotionally, it makes the most sense for him to make that leap at the end of this season, perhaps with another set of medals hanging around his neck.

It would be a blow to lose another England player to a foreign league and in an ideal world I would like to see Harry Kane, Jude Bellingham – and Trent Alexander-Arnold – playing every week in the Premier League. So it would be great to see Alexander-Arnold staying at Anfield. Perhaps if he wins the Premier League and more this season it could compel him to stay but everything is pointing towards him going to Real Madrid. They usually get their way and are masters of the Bosman free transfer. As much as I would love Alexander-Arnold to announce his future with a Wolf Of Wall Street meme declaring “I’m not leaving”, I expect him to join Real in the summer. While Liverpool are fighting for the title, they cannot afford to accept an offer for him to leave during January.