Dyche has been out of work since leaving Burnley in April after 10 years as manager but could well find himself back in the Premier League if the right job becomes available.
What is the latest news from Everton?
It has been a steady start to the season for the Toffees after dodging relegation last term, currently sitting in 13th place heading into the international break.
Wins have been hard to come by for Lampard this term, with just one to his name so far, but they remain unbeaten in their last five top-flight games.
Nevertheless, a big improvement will be expected on last season’s display and performances have continued to leave a lot to be desired.
What has Jones said on Lampard’s possible successor?
Jones understands that, if the Toffees were to sack their manager, Dyche would not be at the top of their list, despite previously being described as an ‘exciting’ boss.
The journalist believes that Everton will look for a figure with global appeal, following a pattern that has also seen Carlo Ancelotti and Rafa Benitez appointed.
Jones told GIVEMESPORT: “It might be a smart way to think but we also know that Everton prefer a certain profile of manager and they like there to be a glamorous element to these appointments. Carlo Ancelotti, Rafa Benitez and Frank Lampard have a global appeal that maybe Sean Dyche does not.”
Would Dyche be a good appointment for Everton?
Jones is right that Dyche would not be a massively exciting appointment, but he could be exactly what is needed at Goodison Park.
After years of managerial changes and underperforming, getting a boss in who can steady the ship and steer them in the right direction makes sense.
With the likes of James Tarkowski and Dwight McNeil making the move to Merseyside from Burnley in the summer, there is also a group of players that Dyche knows extremely well too.
Lampard has picked up two impressive results in recent weeks, but should things deteriorate again, talk of a new boss will almost certainly be on the cards.