City met the Ukranian side in the Champions League last night, and they played out a 0-0 draw.
Yarmolenko had a fairly quiet game, but Martinez and Everton are still reportedly considering making a bid for the exciting wide man.
Everton tried to sign the 26-year-old last summer, but at that stage the deal fell through.
The Toffees have maintained their interest in skilful winger, though, and have continued to discuss the potential to do a deal with Kiev.
With Everton now having a great deal of money to spend, following the investment of Farhad Moshiri, they could step up their interest in Yarmolenko in the summer.
It is believed that Yarmolenko would cost around £25 million (Daily Mail), but he has already expressed an interest in moving to Goodison Park, giving Martinez’s side hope that a deal could be possible.