The Algeria international has previously been linked with West Ham United, but the latest claims suggest Tottenham see the 26-year-old as a viable option as they look to bolster their attacking ranks.
Harry Kane aside, Spurs' front-men have struggled for goals this season, and it would be a surprise if Tottenham manager Mauricio Pochettino did not at least try to rectify that in what remains of the January transfer window.
Slimani has scored nine goals and provided five assists in 20 matches for Sporting this season, and his ability to both score and create could make him an effective option for the North London club.
The latest report does not suggest how much the player may go for, although when he was linked with West Ham a fee in the region of €10million was reported by Italian website TMW.
Slimani’s reputation only increased following his World Cup exploits for Algeria, when he scored against both South Korea and Russia before his country narrowly lost to eventual winners Germany in the first knock-out round.