On announcing Mackay's interim appointment and the upcoming friendly, SFA chief executive Stewart Regan said it was "too premature to discuss" Strachan's long-term successor.
"Recruitment phase begins next week," he said. "It's difficult to put a timescale on replacement.
"We believe we can compete [financially] to get the right person for the manager's job.
"We want someone capable of getting to Euro 2020.
"We'll cast our net far and wide, nationality is not an issue - want best person for the job.
"Ultimately we are in a result business. We had a manager in place for five years coming up. He'd had two campaigns. When the board met to discuss Gordon's position after the defeats to England and Slovakia [in 2016], we backed the manager, but we backed the manager on the proviso that we made the [World Cup] play-offs.
"We didn't reach the play-offs and we felt it was time for a new coach to give us a new impetus with emerging talent coming through the Scottish game and give us a real chance to make Euro 2020."