The eight-man board was due to convene for a regular meeting but Scotland’s World Cup exit means the position of Scotland boss will be high on the agenda.
Strachan’s contract expires next month and pressure is growing in some quarters for the SFA to look elsewhere for a national team boss.
However, Scotland are unbeaten in six games this year since both parties decided to continue with the 60-year-old in charge following an indifferent start to the World Cup campaign.
An announcement on Strachan’s future might not be imminent but the meeting is likely to shape the governing body’s approach to talks with the manager, who may also decide enough is enough after almost five years in the role.
Scotland missed out on second place in Group F on goal difference to Slovakia, who also failed to make the play-offs after finishing with the worst record of the nine runners-up.
Strachan refused to discuss his own situation after Sunday’s 2-2 draw in Slovenia but he stressed how much he enjoyed working with the players.
“I’m the last person I’m thinking about right now,” the former Coventry, Southampton, Celtic and Middlesbrough manager said.
“Players, staff, fans, family, I want to make sure they’re all right. I know the players’ families have backed them up and we are looking after them at the moment.
“Me, it’s not a problem. I am really proud, really proud of the players.”
The SFA board includes president Alan McRae, vice-president and Hibernian chairman Rod Petrie plus chief executive Stewart Regan. Also listed on the SFA website are Partick Thistle managing director Ian Maxwell, Alloa chairman Mike Mulraney, Scottish Amateur FA secretary Thomas McKeown plus businessmen Barrie Jackson and Gary Hughes.
Scotland’s next competitive game will come early next season when the UEFA Nations League kicks off.
Scotland have secured top-seed status in League C, with potential opponents including Greece, Serbia, Albania or Norway from pot two; Montenegro, Israel, Finland or Bulgaria from pot three; and could take on Cyprus, Estonia or Lithuania from pot four.
Success in a three or four-team group would offer a route into a play-off for a place at Euro 2020 if Scotland do not qualify from the conventional group system.