Tuchel, 49, has recently been linked to the England job in the event of Gareth Southgate's departure.
But the former Borussia Dortmund and Paris Saint-Germain coach has reportedly held opening talks with the Ghana FA about becoming the Black Stars' new manager.
Previous gaffer Otto Addo stepped down after his side failed to progress beyond the World Cup group stage.
The ex-Tottenham and Republic of Ireland defender, 64, has worked as a technical advisor to the Black Stars this year.
Hughton, whose father is Ghanaian, has also managed Birmingham and Norwich.
Ghana-born Boateng, 47, has worked as Addo's assistant since May.