Jones, who has taken over from Stuart Lancaster following the failed World Cup campaign, has started to shape his coaching staff.
He dispensed with the services of Andy Farrell, Mike Catt and Graham Rowntree on Monday.
And he has already made approaches for Bristol’s Steve Borthwick and Saracens’ Paul Gustard.
Former Sarries lock Borthwick would take up the role of forwards coach, with Gustard occupying the position of defence coach.
That leaves Jones needing a backs coach, and, according to The Telegraph and The Times, he has made his move for King.
The 40-year-old former Wasps player made the move to Saints from Clermont Auvergne in 2013, replacing club legend Paul Grayson on the coaching staff.
King helped mastermind and Aviva Premiership and Amlin Challenge Cup double in 2014, striking up an excellent relationship with forwards coach Dorian West and director of rugby Jim Mallinder.
He is a popular figure at Franklin’s Gardens, but would have to seriously consider a role with England should Jones offer him one.
Joining King among the favourites for the role as national backs coach is another man with Saints links, Ali Hepher, who is currently at Exeter Chiefs.