Four of Liverpool's summer signings were doing Melwood media duties for the first time on Wednesday. Luis Alberto, Iago Aspas, Kolo Touré and Simon Mignolet all spoke appreciatively of the warm reception they have received at the club and all four dutifully recorded their delight at joining a side so rich in tradition and history.

You know how these things go: they are hardly likely to complain about anything on their first day, are they? Just strike the right tone, say the expected things and get back to training. Everyone expected it but even so all four newcomers were asked how they felt about Luis Suárez, specifically whether the excitable Uruguayan should stay or go.

If you want to know how desperate things get in the dog days of the close season, there's your answer, right there.

Clearly Alberto, Aspas, Touré and Mignolet all said Suárez is a terrific player, because he is. They all said they would like him to stay too, because anyone would. But whether he will or not, who knows?

Certainly not a quartet of newcomers who have been at the club only five minutes and were being asked the question only because Brendan Rodgers is not making himself available. There is no need for the Liverpool manager to do so at this stage of the season, though apparently he will not be answering questions either at the end of the friendly against Preston North End on Saturday. Rodgers is aware that all the questions at any event this week will be heavily focused on Suárez and it would seem from his reticence that at the moment he does not have any ready answers.

What the Liverpool hierarchy are conspicuously not saying is what David Moyes said last week when asked about Wayne Rooney. The new Manchester United manager simply said Rooney would be staying at the club and would not be sold. He wanted to close the matter there, though without any comment from a supposedly disillusioned Rooney it was hard to see that as the end of the story: the ball had simply been lobbed back into the player's court.

With Suárez the ball has never left the player's court. Liverpool have stuck by him in the past, quite rashly at times, yet apart from scripted apologies and club statements Suárez has never publicly accepted that he owes the club any loyalty and would not be tempted by a better offer.

Quite the reverse, in fact. Speaking to a radio station in Uruguay he claimed two or three clubs wanted him and he welcomed Arsenal's interest – despite his previously stated desire to leave the Premier League due to unfair treatment by the English media – because it made him feel valued.

He seems to be suggesting his present club does not make him feel valued and after all that has happened, whatever the rights and wrongs of the Anfield stance when he was accused of being racially abusive, Liverpool hardly deserve that.

Perhaps Suárez knows what many already suspect, that Liverpool have decided to sell him and are simply awaiting the highest bid. That would be understandable, given the number of games Suárez misses through suspension and the amount of money that could potentially be placed on the table, though if the process is reliant on Real Madrid coming through with a big offer to blow any renewed interest from Arsenal, Chelsea or Manchester City out of the water, selling might not be a simple matter.

Suárez would prefer a move to Madrid but the Spanish club know that and are in a position to bide their time and wait until Liverpool become desperate to sell. Without any firm word from the Bernabéu the saga could easily spread out across the rest of the summer. Suárez is out of the country for another 11 days, though not short of news outlets through which to express himself in Uruguay, and is scheduled to join up with Liverpool in the middle of their pre-season tour.

After what he has been saying back home that does not seem the greatest idea and the notion of Suárez actually starting the season with Liverpool grows more unlikely by the day. He is now making little secret of his impatience with affairs as they stand, shrugging his shoulders and accepting that he must return to Liverpool but clearly hoping that the phone call that might change everything will come soon and save him the trouble.

In a possibly misguided attempt to have it both ways, Edinson Cavani recently spoke up on Suárez's behalf, claiming that his "love for Liverpool" is very real. "If they were playing in the Champions League, he would not consider leaving," the Napoli striker said. "But he knows he is now at the stage of his career when he needs to be playing at the top level."

Well said, Mr Cavani. Both realistic and revealing. Harsh yet still fair.

But by my reckoning Suárez still owes Liverpool something. A trouble-free season, perhaps, and with it a proper crack at bringing Champions League football back to Anfield.