Real are in the process of a massive rebuilding process that could yet see Kaka, Franck Ribery and even Cristiano Ronaldo move to the Bernabeu this summer.
And president Florentino Perez has spoken of his admiration, too, for Spanish international Alonso.
'As a fan, I would say that Xabi is a great player,' said Perez. 'I think he is the best passer of the ball in Europe.
'I would be happy [to have him], but I cannot talk about the player without having spoken first to Rafa Benitez, as he is the one who needs to know that we are interested in his player.'
Real's tactics of going public on transfer targets is not a new one though will frustrate Benitez nonetheless.
Uncertainty surrounded Alonso's future at Anfield last summer when Benitez tried to sign Gareth Barry but having missed out on the England international Benitez will now be reluctant to lose Alonso.
However, despite being one of Liverpool's stand out performers last season, Alonso could yet be persuaded that now is the right time to return to La Liga, according to a report in the Daily Mail newspaper.
Meanwhile, Benitez is ready to offer Tuncay a swift return to the Premier League after he was relegated with Middlesbrough last month.
The Turkish international, who was subject of interest from Chelsea during the January transfer window, is likely to be available for around £5 million.
'I have heard something about that,' said Tuncay, 'but there has been nothing official so far. Of course, I would like to play for a big team.'
Though Tuncay would represent value, Benitez has still not given up on his ambition to partner Fernando Torres with Spanish international team-mate David Villa.