4. Sean Dyche
Sean Dyche has won more points against Spurs and Chelsea away from home this season. Koeman has no wins against Spurs since last season, has lost to Burnley twice, and has a 10-0 record against Chelsea (never mind the close loss at the Merseyside derby last season.)
Agreed Burnley's win was probably scrappy at Chelsea, but Dyche has transformed a middling Championship side to one of the hardest to beat sides in the Premier League in a little under five seasons, no mean feat because Burnley's average net spend is around 5.3 million pounds, which is amazing considering that they had to overhaul their squad thrice following a relegation and two promotions.
Dyche is someone who seems popular amongst many Everton fans and seems a realistic appointment. The only doubt would be whether Dyche wants to leave Burnley when it looks at its strongest ever.