Former Manchester United manager David Moyes has been tipped to take over after Scotland manager Gordon Strachan left the post on Thursday.
Strachan was relieved of his job after Scotland failed to qualify for the Russia 2018 World Cup.
Stewart Regan, Scottish FA Chief Executive, said in a statement: “On behalf of the Board I would like to thank Gordon for his excellent service to the national team.
“I know how disappointed he was that we couldn’t secure a play-off place but to come so close was a tribute to the belief he instilled in his squad.”
In a statement released by the SFA Gordon Strachan said: “I said on my first day as Scotland manager that it was the proudest moment of my career and that I wanted to put a smile back on the nation’s face again.
“I share the profound disappointment at missing out on the play-offs, especially having worked so hard to fight our way back into contention.
“The players should receive immense credit for that resilience in coming back from a difficult start and I would like to thank each and every player who has come in to represent their country.
“Together we have shared some really magical moments and those memories will live with me for ever.
“Of course, what made those moments special was the unwavering support of our fans. Through highs and lows you have stayed with the team and my biggest regret is not being able to provide the finals tournament you deserve.
“I would like to thank the Board, the backroom staff and everyone at the Scottish FA for the help and support they have given me as national coach.
“It has been a real privilege.”
Several pundits, including former Scotland star Pat Nevin, have tipped ex-Everton and Sunderland manager to replace Strachan, who coached Scotland for four years and failed to qualify for any major tournament.