Hackney was voted Middlesbrough's Player of the Year and the Championship's Player of the Season following an outstanding campaign as a deep-lying playmaker. He has one year remaining on his contract at the Riverside Stadium and is determined to test himself in the Premier League.
Nottingham Forest had an approach rejected in January, and Hackney turned down Ipswich Town last summer. Crystal Palace, Tottenham Hotspur and Manchester United have all shown interest to varying degrees, but Hackney's preference for Moyes gives Everton a significant advantage in the race, reports the Daily Mail.
The timing of the pursuit aligns with Everton's own midfield needs. Senegalese veteran Idrissa Gana Gueye is 36 and considering his next step, while the club have also fielded enquiries for midfielder Tim Iroegbunam.
Moyes is also looking to strengthen at full-back and striker, and is exploring options for another winger. There remains a chance of a new deal for Manchester City's Jack Grealish, though the scale of financial compromise involved makes that a difficult negotiation to conclude.
Hackney missed Middlesbrough's Championship play-off semi-finals through injury but returned from the bench in the final defeat to Hull City.