The sportswear giants, who manufacture Barcelona’s kit, advertised a Barca shirt on their website with the Brazilian midfielder’s name on it.
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.”
Coutinho is sponsored by Nike and wears their boots.
He handed in a transfer request in August after Barcelona had a bid for the Brazilian rejected, but the Reds then turned down a further two offers.
The current La Liga leaders had offered over £100m, but Liverpool owners Fenway Sports Group publicly stated Coutinho was not for sale.
The 25-year-old missed the start of the season with a back problem but has been in outstanding form recently, scoring seven goals in his last eight games.