The Blues have reportedly agreed a fee of around £13.25million for the forward, with him now having arrived at Finch Farm to complete his medical.
There had been rumours that he was travelling to England earlier in the day, and that has now been confirmed by Echo journalist Phil Kirkbride.
Oumar Niasse at Finch Farm for a medical ahead of proposed £13.5m move— Phil Kirkbride (@philkecho) February 1, 2016
Roberto Martinez will now be hoping there are no complications in the medical, but with the transfer window not set to slam shut until 11pm, they have plenty of time to get the deal done.
It is likely that he will come in as back up to Romelu Lukaku, although he is also comfortable operating on the wings.
The Toffees are short up front at this moment in time, with just Arouna Kone as back up to Lukaku following Steven Naismith's sale to Norwich City earlier in the window.
And Niasse will certainly provide that, having been in decent form in Russia this season, with 12 goals in 21 games for his club so far.