Allardyce has been without a job since leaving Crystal Palace in May but the 62-year-old says that he is not ready for a return to management, despite his links to the nation.
"My parents and sister were all born in Scotland, I have heritage from there, there's no doubt about that," Allardyce told BBC Sport.
Asked if the job interested him, he added: "Not at this moment in time because I'm enjoying not being involved at the front end of football at the moment.
"I think David Moyes would probably be my choice for that one. It's very tempting [for me], but no."
Malky Mackay has been placed in temporary charge of the national side while the Scottish Football Association searches for Strachan's permanent successor.