Burley was sacked from his job as Scotland boss on Monday evening, following their 3-0 loss to Wales at the Weekend.
“We are going to take our time and look extensively, we have a certain amount of time and we want a new manager in place as we go for the European Championship draw in February,” Smith said on Sky Sports News.
“We don’t want to put a timescale on this, the next board meeting we have is early December when we will discuss this matter.
“We haven’t got a shortlist and there will be a lot of speculation, but there will be a procedure, as there was last time. We will sit down with the board of directors and it could be entrusted on the office bearers again to shortlist the candidates and review who might come in as manager, so there is no shortlist or candidates at the moment.
“We will not be discussing any names in the process going forward. I don’t think it is fair to discuss any names in public.
“We will be sitting down to look at the criteria in terms of the candidate going forward, we want someone with experience, authority and a reputation in the game.”