The Algerian has been linked with Tottenham and Leicester recently.
The report claims the Algerian, who has a €30 million (£23.5 million) exit clause, has informed Sporting that he would like to leave and play in another country – with the Premier League looking a likely destination.
It has been reported in recent weeks that Tottenham and Leicester are keen on bringing the player to the Premier League.
Spurs are expected to sign AZ Alkmaar striker Vincent Janssen and are also being linked with a deal for Michy Batshuayi of Marseille – after finding themselves short in the attacking department last season.
Leicester meanwhile are in need of reinforcements as they prepare for a Champions League campaign and also have fears over the future of Jamie Vardy – who has been linked with a move to Arsenal.
Slimani, who has scored 32 goals in 43 appearances in 2015-16, would be a brilliant signing from either club this summer.