Speaking after attending the Emirates Airlines Dubai Sevens tournament, Dodson admitted that the tight timescale – Scotland begin their Six Nations campaign against England at Twickenham on February 2 – would make it very difficult to get a new head coach on board and up to speed in time to prepare the team.
"It is one of the options," Dodson said of a caretaker's appointment. "We have a situation where we don't have a great deal of time between now and the Six Nations. If I'm absolutely honest I would say we would be incredibly lucky to get the kind of person that we want, in time for the Six Nations.
"So we might have to have some kind of interim position. I'm not saying that will happen, but clearly it has to be one of the things that's right there.
"We don't want to take an age to make this happen. We realise there is pressure and we are working to a fairly quick timescale, but I don't want to rush it, either. This role is too important to rush. As far as I'm concerned, I want to get the right guy in the shortest frame of time possible."
The front-runners for any interim role are Scott Johnson, who has been senior assistant coach to Robinson since June, and Sean Lineen, the former Glasgow coach who combines his role as head coach of Scotland's under-20 side with running the SRU's player acquisition function.
Scotland, therefore, find themselves in a position uncannily similar to the one England faced a year ago. Then, in the wake of Martin Johnson's resignation as head coach, Stuart Lancaster, a previously low-key figure, was given the interim job of guiding England through the Six Nations.
Lancaster led England to the runners-up position behind Wales with four wins from five games and his position was later made permanent, despite competition from Nick Mallett, the former South Africa and Italy head coach.
Dodson agreed that any caretaker coach could make a strong case for being handed the job on a full-time basis if he could match Lancaster's record.
However, he stressed that another contender – Mallett has been mentioned in the Scotland context, as well – could still get the permanent job if he was seen as the better option long-term.
Dodson said: "Even though [a successful Six Nations under a caretaker] may happen we still want the best man for the job in the long-term. The most important thing is making sure we deal with the Six Nations first. It would be good to have the person we want in that window, but if we can't we'll play a longer game."
Johnson and Lineen are both backs coaches, so the appointment of either on a temporary basis would still leave a need for a forwards coach, which was Robinson's specialism. Dodson explained that he is considering options in that area, but suggested that Massimo Cuttitta, the former Italy prop who has been Scotland's scrum coach for the past few years, could take on a wider role.
"We could go out and get a forwards coach on a short-term basis," said Dodson. "But we also have Massimo. He is much more than a scrum coach. Massimo could take a huge amount of pressure off whoever takes the role. He has been around the camp a long time and is a very experienced coach.
"At the moment we are just reflecting on where we are and what options are open to us. What people forget is that although it has been the topic of everyone's conversations, it is only a week since Andy stepped down."
Dodson was much firmer on the matter of the Scotland players' performances in a November series in which they lost to New Zealand and South Africa before the humiliating 21-15 defeat by Tonga at Pittodrie that proved to be the final straw for Robinson.
"I spoke to the players in their hotel in Aberdeen," said the chief executive. "I made it quite clear that their performances had not been good enough. I asked them to go away, think about what happened and drive it forward in their club games and also into the Six Nations.
"There was a lack of consistency and a lack of aggression and ferocity that we found unacceptable. That is not going to be tolerated. It's more about consistency.
"We played in patches. We scored three tries against New Zealand, and no-one had done that for a long time. We got ourselves back into the game against South Africa but then we had moments that let the whole performance down. That's what frustrated Andy more than anything – lapses undermined all the good work that had been done.
"As far as I'm concerned, Andy has not only been an outstanding coach, but he has been a great human being, as well. I think the players need to stand up and take a good look at themselves."
On the matter of Robinson's severance agreement – it is widely accepted that Robinson received one, albeit some distance short of what he might have been due had he been sacked – Dodson refused to discuss figures, but did emphasise it would bear no impact on the recruitment budget.
"There has been a lot of speculation about what was or wasn't in Andy's contract. It's not going to make a blind bit of difference to how we are going to progress.
"We are going to get the best possible coach and whatever happens with our budget going forward will accommodate what we need."