Jones is an admirer of Borthwick, who worked with him as a line-out specialist and tactician for Japan, helping them to three victories during the Rugby World Cup, including their shock win over South Africa.
Borthwick's appointment to Jones's management team is a "done deal", but might not be confirmed until next week, with Bristol reluctant to lose the 36-year-old, the Telegraph said.
Jones has yet to announce whether he will be keeping on any of former coach Stuart Lancaster's three assistants - Graham Rowntree, Andy Farrell and Mike Catt.
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(Reporting by Simon Jennings in Bengaluru; editing by Amlan Chakraborty)
