The Premier League duo are keen on the Algerian forward but it will take big money to secure him.
The Foxes have been interested in the striker for some time but new boss Claudio Ranieri has now decided to make their interest serious and will make an approach to sign the player.
It is thought that only a big offer would convince the Portuguese side to part with their man, and the Premier League side are willing to do that by offering £10.4million to get their man.
They would face competition for him though, with Premier League rivals West Ham also thought to be keen on the player according to TMW, as Slaven Bilic looks to add to his squad ahead of his first season at Upton Park.
Indeed, should Leicester make a formal offer for the player, which may force the Hammers to make a move, with it being believed the Croatian manager is keen to add another forward to his squad this summer.
Slimani would likely be a decent addition as well, with him having scored 12 goals in 16 league appearances last season while he also managed two in the Champions League as well.
Whether either side is willing to pay that kind of money for him though, remains to be seen, with the Premier League likely to prove a big step up from the Liga Sagres.
At 27-years-old as well, he would have little resale value, which may make both clubs focus on other targets.