The Toffees are mostly focusing on transfers as they prepare to get busy in the summer window, but Silva needs a new assistant coach at Goodison Park.
Sousa has left Everton to become a manager in his own right, taking over at Portuguese side Famalicao following their promotion to the top flight.
That leaves Everton with a hole to fill in Silva's staff, and Record in Portugal report that Luis Boa Morte is a surprise name in the frame for the job.
Boa Morte, 41, will be remembered by many for his playing days, as he featured in the Premier League as a winger for Arsenal, Southampton, Fulham and West Ham United.
Since then, Boa Morte has turned his hand to scouting for Arsenal and to coaching, working as Sporting's Under-19 boss in the 2014-15 season, beneath Silva.
Boa Morte took charge of Sintrense, a third division Portuguese club, but could now reunite with Silva as his new assistant coach in a surprise move for the Toffees.
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