The Scotland manager had previously revealed he would discover early next week whether he would keep his job after a poor start to the World Cup qualifying campaign and it looks like an announcement will be made on Monday.
The SFA's seven-man board want more time to consider the implications of sacking Levein, whose contract runs until summer 2014.
Levein's job is under threat as Scotland sit bottom of their qualifying group with two points from four matches.
Qualification for Brazil 2014 already looks an insurmountable task and Levein met SFA chief executive Stewart Regan and president Campbell Ogilvie this week to discuss his position.
While appearing as a pundit on BBC Scotland's coverage of the cup tie between his former clubs Dundee United and Hearts on Wednesday night, Levein said: "I had a chat with Stewart Regan and Campbell Ogilvie and I'll find out one way or the other early next week.
"The squad for the Luxembourg game will be named on Tuesday and there will be an announcement before then.
"I'm hugely proud to be Scotland manager and want to continue doing the job."
Scotland face Luxembourg in an away friendly on November 14 and do not have another qualifier until hosting Wales on March 22.
Reports claim sacking Levein now could cost the SFA up to £700,000.
Levein, who took over in December 2009, had already been under pressure after Scotland drew their opening Hampden qualifiers against Serbia and Macedonia, and a double defeat by Wales and Belgium leaves him uncertain of his future.
The former Scotland defender has only won three of his 12 competitive matches in charge.
The SFA board has seven members including Regan, Ogilvie and the two vice-presidents, Hibernian chairman Rod Petrie and former Cove Rangers chairman Alan McRae.
Ralph Topping, who announced he was stepping down as chairman of the Scottish Premier League today, is still on the board.
Businessman Barrie Jackson is a non-executive independent director while Scottish Junior FA chairman Tom Johnston completes the line-up.