Crystal Palace are said to have made a move for the Sporting Lisbon striker.
The 27-year-old has scored 14 goals in 25 matches for the Portuguese side already this season and he looks set to do considerably better than the last campaign, when he netted 15 times in 33 matches.
That followed on from his participation in the 2014 World Cup where he excelled for Algeria, and to date he has a very impressive 20 goals in 41 matches for his country.
The latest report claims Palace made a bid of £15million for Slimani but that Sporting swiftly rejected it.
With a contract until the summer of 2020, if Slimani does leave Sporting in the next couple of years it will be solely down to the club and they know his importance on the field and his value to any potential suitors.
Le Buteur goes on to claim that Slimani could soon be offered fresh terms at his current club with increased wages, suggesting they are well aware of the spending power of Premier League sides and are acting accordingly.
If so that leaves Palace searching elsewhere for a new striker to help maintain their brilliant start to the current season.