Mitchell, after just the one season, is leaving Newcastle at the end of this month.
TalkSPORT says the former AS Monaco director could land a new job immediately with Al-Hilal keen.
Al-Hilal is seeking a new sporting director and Mitchell, along with Liverpool's Michael Edwards, are on the shortlist.
The Saudis have also made a contract offer to Inter Milan coach Simone Inzaghi, with an answer due this week after last night's Champions League final defeat.
In terms of the sporting director position, a decision is also expected this coming week.