Steve McClaren and Slaven Bilic top the shortlist of West Ham United co-owners David Sullivan and David Gold as they plan to replace Gianfranco Zola.
The Sunday Mirror says Bilic remains in charge of Croatia but failed to lead his team to the World Cup finals.
McClaren has rebuilt his reputation with FC Twente and is close to guiding his team to the Dutch title.
A comprehensive defeat at Everton today could still spark his early departure and force the club's owners to find a temporary coach to save the Hammers from going down.