Everton are in talks with Dynamo Kiev to sign Ukraine forward Andriy Yarmolenko for around £14.25m.
Toffees boss Roberto Martinez said the 25-year-old would be a success in England after he scored in Kiev's Europa League win over Everton.
Club officials travelled to Monaco to discuss the transfer with their Kiev counterparts this week.
Martinez is also pursuing a £5m deal for River Plate's Argentine central defender Ramiro Funes Mori, 24.
The signing of Mori would be as an addition to their resources rather than a potential replacement for England's John Stones, who they insist will not be sold after rejecting a £30m offer from Chelsea.
Everton are unbeaten after two Premier League matches this season and entertain Manchester City on Sunday.