Everton owner Farhad Moshiri is said to be a fan of Bournemouth boss Eddie Howe.
Everton are currently searching for potential replacements for Marco Silva, who is under huge pressure.
Silva has failed to live up to expectations at Goodison Park this term, with Everton in 17th place in the Premier League table.
Howe, who is an Everton fan, has support to take over from Silva at boardroom level, with Moshiri said to be a big fan.
However, it is considered ‘highly unlikely’ that Howe would leave Bournemouth in mid-season to take the Everton job.
That could leave the Toffees having to look for other options, as they weigh up their next step.
Silva may well be in borrowed time now, with Everton’s poor run of form showing no signs of stopping, but there is no outstanding candidate to take over.
The likes of David Moyes and Mark Hughes have been linked, but Everton fans do not appear keen on either appointment.
The Toffees are next in action against high flying Leicester City at the weekend, in what looks like another hugely challenging game for Silva’s side.