Speculation had mounted over the future of the national boss following the 3-0 World Cup qualifying defeat in Slovakia on Tuesday night.
The result saw the Scots drop to fourth place in Group F after three games.
Strachan’s side have four points ahead of the trip to play leaders England on November 11, but it is understood that he will be in charge at Wembley next month following discussions with the Scottish FA.
Strachan, 59, is contracted to the job until the end of this World Cup campaign.
He took over from Craig Levein in January 2013 and has been in charge of the national side for 32 matches. He has won eight of the 19 competitive games.
Mark McGhee, his assistant, insists Scotland “still have a great chance of qualification” for the World Cup despite the poor start.
Speaking earlier in the day, McGhee would not be drawn on Strachan’s position.
“I am not going to comment on that,” McGhee said.
“That is for Gordon, not for me. Gordon has his own thoughts. I have not spoken to him, no.
“My only thought I will give you is that there is still a great chance of qualification, obviously results have to improve but I think there is potential there for that to happen.
“So I think it is still all to play for.”