Robinson resigned on Sunday following Saturday's 21-15 loss to Tonga in Aberdeen, a result which saw Scotland fall to 12th in the world rankings as a result of 10 losses in 13 Tests.
Scott Johnson took up his position as senior assistant coach, with primary responsibility for attack, following the 2012 Six Nations whitewash, but the Australian could now find himself in charge for the 2013 tournament, beginning with the February 2 Calcutta Cup clash with England at Twickenham.
Sean Lineen, who won the Grand Slam with Scotland in 1990, is also an option and already a Scottish Rugby Union employee, as head of player acquisition, having been switched from his role as Glasgow Warriors head coach.
Former Scotland wing Kenny Logan would favour Johnson being handed the role on a caretaker basis, following the example set by England last December, when Stuart Lancaster was appointed successor to Martin Johnson.
"It would be silly to try to get a coach for the start of the Six Nations," said Logan, who won 70 caps between 1992 and 2003.
"Do what England have done, see how the players react and what happens.
"I wouldn't rush into getting somebody before Christmas. I'd let the team sweat and see how they perform under Scott Johnson.
"There's not loads of coaches going to jump for the job, it's a big job to take on."
Robinson's coaching team of Johnson, defence coach Matt Taylor, scrum coach Massimo Cuttitta and kicking coach Duncan Hodge remain in their posts.
Johnson, or Lineen, could be given the opportunity to prove their credentials while a global search for suitable candidates is conducted. It is understood expressions of interest have already been made and the formal process could begin by the end of this week.
Led by SRU chief executive Mark Dodson, discussions over Robinson's successor have begun, with Nick Mallett, Jake White, Todd Blackadder, Wayne Smith and Bryan Redpath rumoured contenders.
Some have commitments elsewhere, meaning an interim appointment would make sense.
Although Johnson's time as interim boss of Wales was not an overwhelming success, Logan is happy with his credentials.
Logan added: "If Scott Johnson does well, give him the job. Every coach has got baggage."
Having said his goodbyes to the players and senior officials at the SRU, former Bath and England flanker Robinson may return to address the media before the year is out.
The 48-year-old, who was under contract until after the 2015 World Cup, might have departed sooner following the group exit at the 2011 tournament in New Zealand and the misery of a Six Nations wooden spoon.
He stood firm, arresting a run of seven straight losses with victories in Australia, Fiji and Samoa, but the revival was short-lived.
Defeats this month to the world's top two sides, New Zealand and South Africa, ended hope of a top-eight place at the 2015 World Cup, the draw for which takes place on December 3.
Then the Tonga debacle - along with the Rome loss on March 17 one of the worst displays in living memory - was the final straw and, although he quit, his departure might not have been wholly voluntary.
The players admitted being culpable afterwards, expressing their wish Robinson would stay.
Logan added: "I wouldn't look at him as a failure for Scottish rugby; I think he's been really good for us. He's done a great job as a coach.
"We have got a lot of good quality players and they've let themselves down and let the coach down. They get another chance but the coach doesn't.
"If they'd beaten Tonga he'd still be in a job, probably."
Robinson claimed notable wins against Australia (twice), South Africa, Argentina and Ireland, but was ultimately undone by a poor competitive record - two wins in 15 Six Nations matches, plus the World Cup failure - and the lifeless showing against Tonga.
Blame cannot solely be apportioned at the door of one man, though, according to Logan, who believes more must be done to reform the game in Scotland from grassroots level up.
Having just two professional clubs, in Glasgow Warriors and Edinburgh, may be a factor hampering the Scotland team.
"It's really hard for a coach to do the Scotland job," Logan said. "You can't keep blaming coaches when you haven't got the resources. It's another alarm bell. There are two teams, they need more people playing rugby."
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