Salah has been in red-hot form for Liverpool ever since joining the club last summer from Roma, with 24 goals in his first 30 appearances, including 18 league goals in 22 games.
Currently standing as the Premier League's second top goalscorer, the Egyptian has been heavily linked with a move to Madrid despite joining the fourth-placed Reds just last year.
Former Zamalek chairman Mamdouh Abbas predicted back in November that if Salah scored more than 20 goals in all competitions, he could potentially be worth up to €150m (£134m, $179m), with a move to Spain looking likely to be his next destination.
Egypt's head coach Hector Cuper would later claim in December that he was told of Madrid's interest in Salah.
"I have been told in confidence that Real Madrid are interested in Salah, but we aren't going to get worked up about it," Cuper said. "For me, it is an incredible situation at this point in time."
The latest indication comes from Abou-Rida who claimed Madrid would make an offer for the 25-year-old which if accepted, would be a huge positive for Egyptian football.
"Real Madrid will make an offer for Salah during the summer," Abou-Rida said in a televised interview, as per KingFut.
"Salah is now looking to improve his game, obviously if an Egyptian play for a club as popular around the world as Real Madrid, it is going to great for Egyptian football."
In addition, Salah's agent Ramy Abbas was recently in Madrid to further fuel speculation.
Los Blancos manager Zinedine Zidane has made no secret of his admiration of Salah, speaking about the former Basel man last month.
"Salah is a great player. He showed that at Roma, now at Liverpool," Zidane said.
"He's still young and improving all the time. I don't talk too much about other players, but he is a player I rate a lot."