The Ukrainian has long been linked with a move to the Blues.
A move has yet to materialise however, with the Blues in particular having failed to secure a deal on several occasions so far.
The upcoming summer transfer window could be when that comes to an end though, with Kiev’s chairman claiming that they cannot afford to spoil the careers of players such as Yarmolenko and Aleksandar Dragovic.
“We cannot spoil the career of Andrey Yarmolenko, Aleksandar Dragovic and others who need to be let go,” the Daily Mail reports Ihor Surkis as saying.
“We can look for a replacement, but the primary task is to give a chance to young players.”
Indeed, it seems that Everton are still keen on a move for Yarmolenko as manager Roberto Martinez scouted him against Manchester City earlier this year.
They would certainly have to do that for the winger, with £20million the price he will reportedly be available for should they return with a firm offer.