The Catalan club has repeatedly made hefty bids for the 25-year-old, with the latest bid being reported at £90.5 million.
However, the player responded immediately to that by handing in a transfer request - with the BBC claiming the Brazilian emailed the club with his formal request to leave.
They host title contenders Liverpool at Vicarage Road in their opening fixture of the Premier League season, when fellow England Under-21 global Nathaniel Chalobah and Â£13million Brazilian Richarlison could also make their competitive bows for the club.
But the lure of Barcelona may be too tempting for Coutinho to resist.
The development comes after Liverpool's owners, Fenway Sports Group, released a statement on Friday saying "no offers for Philippe will be considered".
However, Liverpool's stance remains unaltered and his request has been rejected, said reports.
Gary Lineker has told talkSPORT Liverpool were always going to struggle to keep Philippe Coutinho once Barcelona registered their interest in the playmaker.
The German said: "I can't keep players happy".
Barca have plenty of money to spend, having sold Coutinho's compatriot Neymar to Paris St Germain for a world-record £200.6m last week.
The Reds have a vital Champions League qualifier against Hoffenheim in Germany next Tuesday and Klopp will presumably field his strongest lineup in that game, so there may be one or two surprise names in the team that face Watford on Saturday.
Klopp was asked by reporters about Coutinho's position at the club, given persistent media reports that the midfielder would like to move to Barcelona.
Secondly, I think we are light in certain areas of the pitch.
Although it is very hard for any player to turn down the likes of Barcelona and Real Madrid, Nicol has demanded that his former club to stand firm and not sell their prized asset.
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