The Brazilian star was the subject of several bids from Barcelona back in the summer transfer window, culminating in a £105million offer back in August.
But Liverpool refused to sell him, having been left with insufficient time to reinvest the money, and Coutinho remained at Anfield.
Liverpool are now braced for Barcelona to resume their efforts to sign the 25-year-old next summer – or even in January – but could profit from a bidding war between the La Liga leaders, their arch-enemies in Madrid and Paris Saint-Germain.
According to Mundo Deportivo, the reigning European champions have already approached Liverpool to express their interest in Coutinho, who has scored four goals and supplied three assists this season.
With Real’s interest, Barcelona will be keen to wrap up a deal in January, which could drive the asking price up even further.
With Angel Di Maria and Julian Draxler expected to leave next summer, PSG are also in the mix as they search for attacking players and playing alongside compatriot Neymar and young striker Kylian Mbappe could prove enticing to Coutinho.