Los Blancos, who recently appointed Julen Lopetegui as their new manager following the departure of Zinedine Zidane, are reportedly interested in Salah, who had an incredible first season with Liverpool.
According to Spanish outlet Diario Gol, France international Fekir is on Madrid's shortlist as a potential alternative to Salah should the Egypt international decide to remain at Anfield.
The futures of Karim Benzema and Gareth Bale are uncertain, with the latter sparking reports of a potential Bernabeu exit after comments made following his match winning performance in the Champions League final win against Liverpool.
The report claims a potential move for Salah has been made difficult due to the former Roma forward feeling tension with Sergio Ramos after he was injured in a collision with the Spain international during the UCL final.
The report names Fekir as a potential target for Real Madrid, while it also claims a move for Paris Saint-Germain forward Neymar 'is not viable'. Other names mentioned include Sadio Mane and Kylian Mbappe.
The Daily Star also drafted a potential Real starting XI for the 2018/19 season should they be successful in their summer pursuits, which includes Bayern Munich's Robert Lewandowski, who has been heavily linked with a move to Spain.
Fekir, currently in Russia with the France squad for the World Cup, was expected to move to Liverpool until Lyon released a statement revealing that the 24-year-old will not be leaving France.