Peter Ramage and Owen Garvan are among five players who will not be offered new contracts by Crystal Palace at the end of the season.
Crystal Palace boss Alan Pardew reckons it is best for Yannick Bolasie to stay at Selhurst Park for another season.
The SFA have begun the process of recruiting a permanent replacement for Craig Levein, who was removed from the post last month after a poor start to Scotland's World Cup qualifying campaign, which left them bottom of their group with two points from four matches.
Scotland have only had one foreign manager, former Germany World Cup winner Berti Vogts, who failed to impress in the role.
When asked today if they were only interested in a Scottish manager, Ogilvie said: "We want to bring in the best possible manager for the Scottish national team. From wherever, we want the best person for the job."
Ogilvie gave little else away on the SFA's recruitment strategy.
"The process is well under way and obviously it's our aim to have a new manager in place in plenty of time before the next competitive game in March against Wales," he said.
"We have got some individuals who we believe could fill the post. I'm not going to get drawn on any details."
When asked if they had approached any candidate, he said: "All I'm going to say is we are working on the process and we will come out once we have a decision finalised."