The Algerian hit-man shone over the summer at the World Cup, firing two goals for the North Africans as they advanced to the knockout phase.
He was in demand after the tournament, but despite interest from the likes of West Ham, Leicester and Crystal Palace, Sporting were able to hang onto their man.
And now reports have revealed that the Hammers are back in the hunt for the 26-year-old, with representatives from the east London club having travelled to Portugal to thrash out a deal.
Even with Andy Carroll back from injury to compete with summer signings Enner Valencia and Diafra Sakho for game time, Sam Allardyce wants to add more goals to his team in a bid to maintain the Irons’ surprise push for a top four finish.
Slimani may be a replacement for wantaway newbie Mauro Zarate, who has set his sights on a transfer as he looks to push his way into the Chilean national side.
Sporting want around £8m for Slimani, whose contract in Lisbon is set to run until 2017.