The former Liverpool man was part of Koeman's coaching staff at Southampton.
The Southampton assistant will not be following Ronald Koeman to Everton.
England and Southampton coach Dave Watson as well as Sammy Lee have no plans to join Everton.
The Southampton boss is expected to take the reins at Goodison Park this week.
The Toffees look set to appoint the Southampton manager, but could he bring an unwanted guest with him?
Southampton boss Ronald Koeman "knows all the tricks" for success in Europe, says former player Jimmy Case.