The Brazilian has always been on Barcelona's radar as they sought a replacement for Neymar, who moved to PSG, and are believed to have had a £90m offer rejected by the Reds.
Fenway Sports Group, which owns the club, released a statement shortly thereafter saying that no offers for Coutinho would be considered despite his request to leave.
The Reds have rejected two bids from the Spanish giants in recent weeks and it was revealed last week he would be interested in making the switch if a deal could be reached amicably between the two clubs.
But shortly afterwards, the Liverpool Echo reported that Coutinho had sent an email to Liverpool's sporting director Michael Edwards expressing his wish for a move.
"Liverpool is not a club that has to sell players".
Speaking at an earlier news conference previewing the league match at Vicarage Road (12:30 BST kick-off), Liverpool boss Jurgen Klopp said the Brazilian would miss the season opener because of a back problem.More news: Guam's worries grow as tensions rise between US, North Korea
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The Liverpool manager added: "Today, no player on the planet is untouchable".
"When FSG say something like this it is 100 per cent clear", said Klopp.
Here, we look back at the key dates this summer in Barcelona's pursuit of the Reds star - with the Catalans twice being knocked back with big-money bids.
The German said: "I can't keep players happy".
"It is not for you, it's between me and all the boys, not just Philippe".
Sturridge was quick to play down fears of a lengthy layoff, but he will sit out the season-opening clash against Watford on Saturday as Klopp wants him ready to take on Hoffenheim in Tuesday'sChampions League qualifier.
Coutinho, who joined Liverpool from Inter Milan for £8.5m in 2013, signed a new five-year deal with the Merseyside outfit in January that did not include a buy-out clause.