He is staying, they have insisted, no matter who is interested. They have been reassured by the sounds from the striker that he is happy to remain on Merseyside.
Now the hints from the Uruguayan's camp are different. Suarez is imagining an environment where he does not feel he is persecuted.
If that invites questions as to where his various misdemeanours are tolerated, and why they should be, the essential issue for Liverpool today is a footballing one: what does a side shorn of Suarez look like and where do the goals come from?
As his 10-game suspension for assaulting Branislav Ivanovic begins, Suarez will not be seen in a red shirt again in a competitive fixture until September, if at all.
A campaign that has included 40 games, 30 goals, 213 shots and umpteen occasions when he has made a defender look foolish has been brought to a premature end.
The fault is Suarez's but the problem belongs to Brendan Rodgers.
For a select group of clubs, in no danger of relegation and unlikely to qualify for Europe, the end-of-season fixtures can have an experimental feel.
If all Liverpool can realistically hope to achieve is to win the Merseyside derby and leapfrog Everton to claim sixth place, their final four games will acquire a greater significance if Suarez does depart.
Even if he remains, they have an added importance, not least for Daniel Sturridge.
While Fabio Borini, who has been out for two months, could be back on the bench today, Rodgers is again down to one senior striker who can start.
The last time Liverpool were without Suarez for an extended spell, Kenny Dalglish could call upon Andy Carroll, Craig Bellamy and Dirk Kuyt. Now, Sturridge is, by default, an automatic choice today. While it is not why it will be remembered, the £12 million (Dh68.1m) forward transformed last Sunday's game against his former club Chelsea as a substitute.
"He was outstanding when he came on," Rodgers said. "He gave us a real threat: his pace and power were outstanding.
"He scored a goal which was a great finish and could have had two or three more.
"He's got the potential to be a top European striker and that's hopefully something he can fulfil here."
Despite that heady praise, Sturridge has had a stop-start Liverpool career.
Whereas before the question was how to accommodate Suarez and Sturridge in the same side without Liverpool being outnumbered in midfield, now the issue is whether the Englishman can shoulder the burden of leading the line alone and providing the clinical touch.
When nearer match fitness, that responsibility will be shared with the injury-prone Borini, whose nine months at Anfield have brought just nine league games and no goals.
Should Suarez stay put, they will become pivotal again in August. Liverpool have a habit of starting seasons slowly.
This has been the third campaign in four years where they have been playing catch-up from the early weeks onwards, usually unsuccessfully.
If they are to fly out of the blocks in 2013/14, others have to provide the impetus until Suarez is eligible.
Perhaps, however, he will be employed elsewhere then. So it provides unfortunate parallels for Liverpool.
The last time they visited Newcastle United, there was the sense things were falling apart.
In one of the lowest days of Dalglish's second spell in charge, they lost 2-0 a year ago with Pepe Reina sent-off for butting James Perch.
Left-back Jose Enrique donned the gloves and, so abject was their performance, one writer that day named him Liverpool's man of the match for his goalkeeping.
Twelve months on, their performance level is rather better but their season is petering out again. Suarez has been its dominant figure.
Now, without him, there is a void, no hero or villain, with less controversy or quality. It is the lull after the storm.
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