Coutinho even put in a formal request for a transfer to Barcelona.
Liverpool rejected three mega-money bids from Barcelona and the Spanish side are expected to make further offers in January.
The sportswear giant, who manufacture Barcelona's kit, advertised a Barca shirt on their website with the Brazilian midfielder's name on it.
Philippe Coutinho rumours have been spreading since the first inklings of Barcelona's interest in the summer, but they are set to go into overdrive now that the Premier League transfer window has reopened.
The Reds will not have been impressed with Nike's blunder and Klopp refused to be drawn into a discussion on the subject after Liverpool's win over Burnley.More news: When can you see the 'wolf moon' in New Orleans?
Headlined "Where the magic happens", the page, which has since been taken down, continued with the message: "Philippe Coutinho is ready to light up Camp Nou".
'Get your 2017/18 FC Barcelona kit with the Magician's name on it. Act fast-free personalisation only available until 6 January'. I can't tell you about it, though, because for different reasons I couldn't be less interested in anything in the world.
There were suggestions before the game against Burnley that Coutinho had been excluded due to the speculation surrounding his future.
The Brazilian has been in stunning form once again this term, scoring twelve goals in all competitions for the Reds.
For now, though, Coutinho's focus will be on this Friday night's mouth-watering FA Cup clash against Everton at Anfield.