Following Arsenal's rejected bid of around £30 million for the Uruguayan, Suarez's agent, Pere Guardiola, spent Monday on Merseyside in discussions with manager Brendan Rodgers and managing director Ian Ayre.
There were two meetings, the first with Ayre at the club's Chapel Street office in Liverpool City Centre and then a secondary discussion with Rodgers at Melwood, Liverpool's training facility.
No transfer request was issued on Suarez's behalf, although it was made clear the 26 year-old continues to harbour concerns as to whether his career can move forward on Merseyside.
It is understood the conversations were amicable and encouraging, Liverpool holding Guardiola in high regard as they do not believe there is currently any underhand attempt by Suarez or his representatives to broker a deal behind the club's back.
Liverpool are relaxed that Suarez does not seem - at this stage at least - as eager to force through a transfer as recent interviews in Uruguay suggested.
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As yet, Arsenal's formal approach for the striker is the only firm offer received and, as expected, it was immediately rejected by Liverpool.
Suarez expects to be kept informed of all interested parties and Liverpool will have a duty to inform him if any club bids £40 million, but there remain numerous obstacles in the way of his exit, not least the absence of bids anywhere near his valuation.
Neither party is in a position to state whether Suarez will remain a Liverpool player beyond this transfer window, however, but the absence of a bid from Real Madrid has offered some hope Rodgers can persuade Suarez to stay in England for one more year to see if he can assist in returning Liverpool to the Champions League.
Rodgers will need all his skills of diplomacy to do so, but it should not be underestimated how eager Liverpool are to retain Suarez's services. Indeed, there is some agitation at the highest levels of the club whenever it is suggested that the board would not be too unhappy at cashing in for £40 million. If that was the case, Liverpool could have opened negotiations with most of Europe's major clubs weeks ago in order to start an auction.
If Suarez leaves, Liverpool will be most reluctant sellers.
Further discussions with Guardiola are planned as Liverpool have also made it known that if Suarez does ask to go, and an acceptable offer made, there is no wish for the situation to drag into August.
Liverpool have been stung too often by high profile players using the last days of the transfer window to secure their moves, leaving the club with little or no time to find a replacement.
There are long memories at Anfield. In 2004, Michael Owen left Liverpool on the final day of the transfer window and the manager at the time, Rafa Benitez, had no choice but to accept the undistinguished Antonio Nunez and a paltry £8 million from the deal. He had to wait six months to buy a goalscoring replacement, Fernando Morientes.
In January 2011, Fernando Torres' sale to Chelsea was also completed on deadline day, and Liverpool's subsequent decision to bid for Andy Carroll is now recognised as one of the costliest transfer mistakes in English football history.
Liverpool are anxious never to be in the same position again, although the longer the situation drags on without a statement from the player clarifying if he will stay or go, the more concern there is history will repeat itself.
Rodgers, meanwhile, could raise even more transfer funds by selling Stewart Downing to West Ham for £8 million.
Sam Allardyce has contacted Liverpool about the player. There is no bid yet, but negotiations are continuing between the clubs.
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As far as agents go, Pere Guardiola seems quite a reputable bloke and if Suarez is still hellbent on leaving then I'd imagine he'd ensure his fella is out of the club by August. Of course this doesn't factor in Madrids agenda, Michael Owen for 8M and fecking Nunez, we've been screwed over by this outfit before and I hope Guardiola can appreciate this and along with Rodgers talk a bit of sense into him - hand in the transfer request (something he hasn't done) and leave now, or sit tight and help fire Liverpool into the CL next season.
Champions of England 2020.
YNWA