"But we're confident both the coaches will be in place for when we need them."
After the RFU swooped to prise Jones from the Stormers after the 2015 World Cup, there would be a certain sense of deja vu about any approach for Mitchell, who was appointed Bulls coach only in May after a short spell in charge of the United States.
Reports in South Africa suggest Mitchell is already at loggerheads with his board over his demands for a bigger playing budget and has not signed a contract extension.
In a tweet, the Bulls confirmed that an unspecified approach for Mitchell had been made.
"The Blue Bulls would like to confirm that John Mitchell informed us that interest was shown in his services. No formal offer has, however, been received," the Bulls said.
"The [Blue Bulls] would furthermore like to confirm that John Mitchell's contract expires on October 31, 2019."
Mitchell previously coached England as forwards coach under Clive Woodward from 1997 to 2000 and has also coached Sale Sharks and New Zealand.
The 54-year-old New Zealander may even rival Jones for possessing the most ferocious reputation in the game.