The Sporting Clube de Portugal front man is also being hunted by Stoke City and Newcastle are rumoured to be ready to join the race for his signature.
But ClaretandHugh understands that manager Sam Allardyce still has to convince himself 100 per cent the player is physically suited to the rigours of a long Premier League campaign.
At 6ft 1 in he is the sort of striker that the manager likes to work with but the club are currently weighing up his physical credentials alongside several other targets.
A source told us: “It’s a big issue in Sam Allardyce’s world. It’s perfectly reasonable to come to a conclusion on whether he is an individual who is up to a long Premier League campaigncan do it over nine months.
“Slimani is just one name on the rather long short list and the club won’t rush into decisions – they still have time on their side.”