Coutinho was subject to various bids for from the Blaugrana and he remains unsure about his future at the Anfield.
Coutinho started the season in dispute with Liverpool, which refused to sell him to Barcelona following repeated bids by the Spanish team in August.
The Brazilian bagged his first ever Champions League hat-trick and was sensational as Liverpool booked their place in the knockout rounds of Europe's premier competition.
"His dream move to Barcelona didn't materialise in summer, but we're taking no risks on Philippe Coutinho being granted his wish in January after reports Liverpool have agreed a deal with the Catalan Giants", said Mr Algar.
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Former Liverpool striker Michael Owen has compared Liverpool's current attacking quartet of Salah, Mane, Firmino and Coutinho with that of the famous 2013-14 season with Suarez, Sturridge and Sterling. What will happen in January, we will know it in January.
Handed the captain's armband for Liverpool's crunch meeting with Spartak Moscow in the Champions League on Wednesday, Reds attacker Philippe Coutinho put in a performance worthy of the position bagging his first European hat-trick for the Anfield outfit.
Coutinho: "Last summer there was a job offer in the same way that happens with any employee and I was interested in it".
Barcelona are being widely tipped to return with a big-money offer in the January transfer window.
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Coutinho has shown his versatility under the management of Jurgen Klopp and has transformed into arguably one of the best playmakers in World football.
I'm very happy to play alongside all these great players.
"Of course a lot happened in the summer but my will is always to play and do the best wherever I am - that has not changed. I do not know if there will be an offer", explained the Brazilian, being completely frank.
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