Slimani, 27, starred in his native Algeria with CR Belouizdad, before moving on to Portugal with Sporting Lisbon back in 2013 - and he hasn't looked back since.
The 6ft 2in striker scored ten goals in his first season for the Sporting, and followed that up with 15 goals in all competitions last season, making a big improvement.
Now under new manager Jorge Jesus, Slimani has started the season in superb form, scoring eight goals in 19 appearances - and his exploits are seemingly attracting interest.
Algerian newspaper Le Buteur report that Tottenham and West Ham, two teams who have had a long-standing interest in Slimani, are once again looking to sign him during the transfer window, as they look to improve their attacking options.
However, it's stated that Slimani has a €40m (£28.4m) release clause in his contract, and Sporting will refuse to sell for anything below that figure.
That's an astronomical fee for a 27-year-old striker who is unproven outside of Algeria or Portugal, meaning both Spurs and West Ham may have to look elsewhere.
The Hammers don't necessarily need attacking reinforcements given that Slaven Bilic has the likes of Diafra Sakho, Enner Valencia, Mauro Zarate, Andy Carroll and Nikica Jelavic at his disposal, but Slimani could be a top target if any of those players were to leave or suffer an injury.
Meanwhile, Spurs clearly still need a striker to help ease the burden on Harry Kane, and an experienced forward like Slimani, who boasts impressive aerial ability, would be a potentially ideal player to come off the bench and offer something different to Mauricio Pochettino's attack.
Either club would have to stump up big money though, and many fans would argue that spending money on QPR's Charlie Austin would be a better move, considering his proven Premier League record.