Since moving to Anfield in a club record transfer over the summer, the 25-year-old forward has been in inspired form.
Salah already has 17 goals to his name, while helping his country to reach the 2018 World Cup, with his efforts drawing comparisons to former Reds star Luis Suarez.
His performances have thrust him under a global spotlight, and La Liga champions Real are among those now reported to be closely monitoring his situation on Merseyside.
“To me, he is in an amazing position right now.”
Cuper is not the first to suggest that Salah could be destined to make a move to the Spanish capital.
He said: “Salah has got the mentality to keep playing at the top level for many years.
“I believe that Salah will not stay for long at Liverpool. Soon he will be gone to Real Madrid.”
While his form is earning him plenty of plaudits at present, Salah has also been urged not to rush any decision regarding his future.
Former Zamalek owner Mamdouh Abbas said of his fellow countryman on Twitter: “Mohamed Salah is currently an institution in Egypt and has an efficient agent working to get the best for the player.
“Salah highly respects those in charge of his finances and as his agent has discussed with me, we agree that Salah should stay at Liverpool until the end of the season.”