The Blues will reportedly make a move for the Newcastle United midfielder this week.
New Toffees manager Ronald Koeman is expected to be busy in the transfer window as he looks to improve the squad he inherited from Roberto Martinez.
He has reportedly been handed vast transfer funds by shareholder Farhad Moshiri, who is keen to turn Everton into Champions League contenders.
So far Koeman has only secured the signing of goalkeeper Maarten Stekelenburg but more arrivals are expected.
And according to the Daily Mail, the former Southampton manager has made the capture of Newcastle star Wijnaldum a priority signing.
He was keen to sign the player while in charge of the Saints but the forward elected to join Newcastle instead.
He retains an interest in his services though and now wants to bring his compatriot to Merseyside, with Everton expected to make an approach this week.
Newcastle are likely to prove hard sellers though, with their manager Rafa Benitez determined to keep hold of his star players such as Wijnaldum and Moussa Sissoko following their relegation to the Championship.