The administrators have had talks with manager Ally McCoist about the potential impact of the crisis on the playing staff and said that Chief Operating Officer Ali Russell had also agreed to leave the club.
"It is clearly understood by all, including the players, that the football department costs will come under review as is the case with all departments within the business," said Paul Clark of administrators Duff and Phelps.
"No decisions regarding staffing in any department have been taken at this point and will not be taken until next week," he added.
Smith and Russell will stay on until the end of the month.
Rangers, one of the best supported clubs in British football, went into administration last week after authorities pursued them for nine million pounds in unpaid sales and payroll taxes dating back to the takeover of the club by businessman Craig Whyte last May.
Smith, a former Rangers player, left with a parting swipe at Whyte, saying he was not allowed to do his job properly and focus on areas like transfers and youth development.
"I wasn't in control of any of these activities despite constantly making it clear to Craig Whyte that this was to be my remit," he said in a statement released by Duff and Phelps.
"I outlined my medium to long term strategies for the club on numerous occasions to no avail. There's no point in being a Director of Football unless you can control these areas, so, in that respect I'm totally comfortable with being made redundant at this time," he added.
Rangers, Scottish champions a record 54 times, have effectively surrendered their title to local rivals Celtic after suffering a 10-point deduction. They are second, 20 points behind Celtic who have played a game more.
