The 25-year-old is believed to be on the verge of undergoing a medical with the Premier League club as manager Roberto Martinez looks to increase his options in attack.
He already sanctioned the £8.5m sale of Steven Naismith to Norwich City this month, while winger Aiden McGeady is closing in on a loan spell to the Championship.
Niasse is undergoing talks in hopes that he can agree personal terms with the Toffees in order to secure his dream move to the English top flight.
The forward was voted the Russian Premier League’s player of 2015 after managing to register 12 goals from a total of 21 appearances for Lokomotiv.
He was also linked with other clubs in England, but is highly tipped to finalise the terms of his switch to Goodison Park later today.