The Egyptian has become a hero in Anfield since arriving in Merseyside almost two years ago.
But now, according to Spanish channel AS, he is determined to force the club out this summer.
Reports say Salah has asked Premier League leaders to sanction their sale at the end of the season.
It comes as a result of a series of heated discussions with Liverpool boss Jurgen Klopp, the newspaper said.
The Egyptian is even willing to hand over a transfer request to force the move.
Salah signed a new five-year contract with the Reds last summer after a record season at the club.
En route to beating PFA Player of the Year, he scored 32 times in the Premier League, the highest number of goals ever in a single campaign.
He also helped Liverpool reach the final of the Champions League in Kiev, where he injured his shoulder in an embarrassment with Sergio Ramos.
Real Madrid will be just one of the few clubs around the world that will be able to afford it if he can leave Liverpool.
A great indication of whether these reports are true will be if the striker starts for the Reds tonight in Porto.
Liverpool take a 2-0 lead at Estádio do Dragão as they try to reach the semi-finals, where they will meet Barcelona.
Salah returned to form before the showdown, having scored two impressive goals in the last two Premier League games.
That included a 25-year stunner after Kepa Arrizabalaga during Sunday's 2-0 win over former Chelsea club Anfield.
He is now at the same level as Sergio Aguero at the top of the 19-point Premier League table.
Salah took the chance to explain his celebration, which was a big point of discussion during the win, which put him two points clear at the top of the table.
"I am a yoga man! I do yoga and it came to mind, "Salah told Sky Sports.
"Usually I shoot with the inside of my foot. But this one I decided, because it was far, to hit him with power. I was lucky because the ball hit the net like that. "
Salah's agent, Ramy Abbas Issa, was quick to close the reports.
He tweeted, "Speaking of your AS again I see."
The position of Liverpool around Salah is clear, they see him as one of their most valuable assets and want him to help them win trophies.