The Toffees are growing impatient with the Belgium midfielder, a report claims.
The report claims Zenit's Witsel has been in talks since mid-June
It is claimed the Toffees previously felt confident of landing Witsel, with whom they've been in talks since mid-June, however, his contractual demands have held up the deal.
And Ronald Koeman's side are already going after alternatives it seems, with the Echo backing up earlier reports of an enquiry for Newcastle United midfielder Moussa Sissoko.
Newcastle's Sissoko impressed at Euro 2016
Roma's Kevin Strootman is another player named as having been discussed, should Everton give up on their pursuit of the Napoli- and Inter-linked Witsel.
Everton have added just one new face so far, with Dutch goalkeeper Maarten Stekelenburg joining from Fulham for an undisclosed fee.
Stekelenburg is Everton's only summer recruit
The recent appointment of Steve Walsh as director of football may accelerate the Toffees' recruitment drive, however.
The 51-year-old, whose brother Mickey played for the Merseyside club briefly in the late 1970s, has gained a reputation as one of English football's top talent spotters, having discovered Jamie Vardy, Riyad Mahrez and N'Golo Kante for Leicester City.
Walsh has left his dual role at Leicester assistant boss and head of recruitment