Salah joined Liverpool from AS Roma in the summer, and the 25-year-old has scored 16 goals in 20 appearances for the Merseyside giants during the 2017-18 campaign.
According to Salah's national team manager, Madrid are closely monitoring the attacker ahead of a potential move in next summer's transfer window.
"I've received confirmed news revealing Real Madrid's interest in Salah, but let's not rush things," Cuper told ON Sport TV. "To me, he is in an amazing position right now."
Salah signed a five-year contract with Liverpool upon his arrival during the summer.