The 25-year-old wants to move on from the Etihad this summer after failing to nail down a place in Pep Guardiola’s starting eleven.
With Manchester City trying to sign Marc Cucurella from Brighton, the Ukrainian is expected to be sold in the ongoing transfer window.
Arsenal and West Ham have shown an interest in getting their hands on the left-back in the coming months.
But it has been claimed Everton are now the keenest to sign the Manchester City left-back this summer.
Frank Lampard is looking to strengthen key areas of his squad after Everton barely survived in the Premier League last season.
The Everton manager wants a new full-back and Zinchenko has emerged as one of the top targets for the club.
The Ukrainian’s ability to play in midfield is also something Everton admire and Lampard wants that kind of versatility in his squad.
Pep Guardiola is prepared to sell Zinchenko as long as Manchester City get an acceptable fee for him.