Manager Roberto Martinez wants greater attacking options after selling Steven Naismith to Norwich and Aiden McGeady also possibly going out on loan.
Everton's top target was Dynamo Kiev forward Andriy Yarmolenko but they have been frustrated in that pursuit.
Senegal striker Niasse has 12 goals in 21 games for his club this season.
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Everton have made an approach for Lokomotiv Moscow forward Oumar Niasse and hope to tie up a £13.5m deal before Monday's transfer deadline.