However, according to the former Inter Milan midfielder's agent, he has not been in contact with either Spanish club and Coutinho has no desire to leave Anfield.
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As per the Mail, his agent Kia Joorabchian said: "Philippe is extremely happy at Liverpool. He signed a new long term contract towards the end of last season that represents his ambition and his feeling for Liverpool.
"Reports that I have been talking to Real Madrid about Philippe are not true.
"His aspirations are to qualify for the Champions League with Liverpool this season and to win a trophy. That is all that he is focussed on – and nothing else."
In what has proven to be a turbulent fortnight for the Reds, that has seen Brendan Rodgers get the chop, the risk of losing their midfield maestro seemed very real.
But with the prospect of Jurgen Klopp taking over on Merseyside, the news that Coutinho is not considering leaving the northwest will be a huge bonus to the Anfield faithful.
Having lost Suarez and Raheem Sterling in recent summers, it will come as a bonus to see Coutinho is in no rush to end his stint at Liverpool.
The club will also be hoping they can drop the 'selling club' tag they have picked up in recent years.
If Liverpool are to enjoy any success this season, or in the recent future, the 23-year-old will be integral to their plans. And, this news will come as huge bonus for whomever takes the reigns on Merseyside.
Will Philippe Coutinho stay at Liverpool if they fail to qualify for the Champions League? Have your say in the comments section below!