Mitchell, after just one season, leaves Newcastle at the end of this month.
Talksport says that the first as a monaco director could immediately get a new job with Al-Hilal Keen.
Al-Hilal is looking for a new sports director and Mitchell, together with Michael Edwards in Liverpool, is on the shortlist.
The Saudis also made a contract offer to Inter Milan coach Simone Inzaghi, with an answer this week after the last defeat of the Champions League last night.
With regard to the position of sports director, a decision is also expected this next week.