According to the British newspaper, Portuguese giants Sporting value the Algeria international centre-forward at about £10.5 million.
The Sunday Times claim that West Ham are looking at Slimani as an alternative to Atletico Madrid striker Raul Jimenez.
The Mexico international reportedly failed to turn up for a medical at the Hammers on Friday because he overslept.
Good signing for West Ham United?
Slimani is a highly-rated striker and one of the best in the Portuguese first division.
Signing the 27-year-old would be a good move for West Ham, who need more firepower up front in order to finish in the top eight of the Premier League this season.
It remains to be seen if the London outfit are willing to pay as much as £10.5m for the services of Slimani.