The Telegraph says Boehly has promised Tuchel full control of transfers. American investor Boehly is desperate to follow the business model of Premier League rivals Manchester City and Liverpool.
Pep Guardiola and Jurgen Klopp have transformed their sides into European powerhouses in recent years.
The duo have built squads based around their playing philosophy, resulting in plenty of silverware.
And Boehly is eager for Chelsea to follow suit under Champions League winner Tuchel.
Giving the German the say over dealings will allow Tuchel to finally build a squad perfectly designed for his possession-based 3-4-3 formation.