According to reports, the Spanish giants approached the two Premier League stars to discuss possible transfers after failing in their pursuit of Eden Hazard and denying making moves to sign either Neymar or Kylian Mbappe from Paris Saint-Germain.
The European champions were in the market for elite forwards to boost their attack. However, Salah signed a new contract with Liverpool before the World Cup, as did Kane with Tottenham, and neither were tempted to move.
Madrid have since focused their attention on getting behind Gareth Bale as their star man.
The La Liga outfit have been impressed by the striker who scored nine times in 14 appearances on loan to Borussia Dortmund last season.
The lure of Champions League football certainly sweetens the deal for the 24-year-old as well as Chelsea will miss out on the same this term.
With the Blues actively seeking to rope in another striker, the Belgian international is desperate for another loan spell away from Stamford Bridge.
Having already signed Bernd Leno, Sokratis Papastathopoulos, Lucas Torreira and Matteo Guendouzi this summer, the new Gunners boss has already gone through most of his transfer budget.
Emery is determined to recruit N’Zonzi though who played a part in France’s World Cup triumph in Russia this summer.
The Spaniard must decide which players from his current crop he will part with before the club sanction a move for the Sevilla midfielder.