John Jeffrey is a former Scotland international

The SRU will next week start interviews with candidates to succeed Matt Williams, who was sacked in March after winning just three Tests from 17.

Interim coach Frank Hadden is favourite to be appointed, BBC Sport understands.

Edinburgh Gunners' head coach guided Scotland to wins over the Barbarians and Romania in the summer.

Jeffrey and Rutherford will join SRU president Andy Irvine, chairman Allan Munro, chief executive Gordon McKie and non-executive director Brian Kennedy on the selection board when interviews begin.

Both men have given distinguished and illustrious service to Scottish rugby SRU chief executive Gordon McKie

McKie said: "We have received a number of applications for the post of Scotland national coach and the interviews commence next week.

"To assist in that overall process, we have secured the services of John Jeffrey and John Rutherford.

"Both men have given distinguished and illustrious service to Scottish rugby beyond their momentous playing careers and each has since acquired high-level rugby coaching and wider team management experience.

"I believe their involvement will assist in our decision-making for the appointment of our national coach - a crucially important role for the game in this country."

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There had been reports that Hadden's trial period would be extended to the autumn Tests against Argentina, Samoa and New Zealand.

But this has been denied by the Scottish Rugby Union.

Hadden's stock rose further at the weekend after guiding Edinburgh to an opening Celtic League win away to the Scarlets.