Sale are currently bottom of the Aviva Premiership after suffering six successive defeats.
It is their worst start to a Premiership campaign, and the club last month parted company with forwards coach Steve Scott.
Sale have so far made no comment on a possible move for Mitchell, which was reported in the Sunday Times.
It is understood, though, that he could either slot in as a direct replacement for Scott or take a more wide-ranging coaching consultant's post.
Mitchell is a former Sale player and rugby director who left the club to work as part of Clive Woodward's England coaching team.
Mitchell returned to New Zealand in 2001 and coached the All Blacks at the 2003 World Cup tournament in Australia that England won. New Zealand made a semi-final exit.
He went to become Perth-based Super Rugby franchise Western Force's head coach, and has latterly been working in South Africa.
Mitchell, though, is currently involved in legal action against his current employers the Golden Lions in Johannesburg, having been suspended three months ago amid allegations from players that his regime was too harsh.
It is believed that any move to Sale will not be finalised until after his legal action has been completed.
Sale now enter two weeks of Heineken Cup action, entertaining Cardiff Blues and then visiting French club Montpellier.
The Sharks' next Premiership game is away to Worcester on October 26.
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