After a season away on-loan with AS Monaco, Slimani is up for sale at the Foxes this summer.
A return to Sporting has been mooted for the Algeria international, but they now face competition from local rivals Benfica.
A Bola says new Benfica coach Jorge Jesus has requested the board move for Slimani. The pair worked together at Sporting.
And it's suggested the presence of his old coach could swing Slimani's thinking in Benfica's favour.