The BBC is reporting that Mitchell is understood to be Jones' number one target to replace Paul Gustard as England defence coach.
Mitchell is head coach at the Blue Bulls Super Rugby side in Pretoria and was assistant to Clive Woodward with England between 1997 and 2000.
The 54-year-old's contract in South Africa runs until 2019, so an early release would need negotiating.
England have been without a defence coach since Gustard's departure to Harlequins following the tour of South Africa in June.
