Arsenal are reportedly desperate to sign a striker before the summer transfer window closes.
Reports emerged on Monday suggesting the Baggies had submitted a club record £21 million bid for the Algerian, but that offer has been rejected by the Portuguese giants, who value Slimani at £26 million.
Swansea and Everton have also been mentioned as possible suitors, while Arsenal were understood to have looked at the striker earlier in the summer after being snubbed by Leicester City striker Jamie Vardy.
The Gunners were handed a devastating 4-3 defeat at home to Liverpool on the opening day of the Premier League season, with boss Arsene Wenger coming under increased pressure from fans over his transfer policy.
While Sunday's loss suggested Wenger may well be in the market for a defensive reinforcements, the Daily Star claims that a striker is also near the top of the club's priorities in this transfer window.
And they may well feel that Slimani has all the hallmarks of a top Premier League striker, having notched 32 goals in all competitions for club and country last season, while also boasting a record of 56 goals in 107 games for Sporting over the last three years.
But with West Brom boss Tony Pulis also placing a forward at the top of his summer shopping list amid Saido Berahino's increasingly likely exit, Arsenal may have to move quickly if they are to avoid missing out on another target.