The former manager have told some club sources that he will walk away from Ibrox if current boss Ally McCoist is forced out, according to BBC Sport.
Smith took on the position three months ago in an effort to help move Rangers forward, but has reportedly been left dismayed by the treatment of McCoist in the last 72 hours.
McCoist has been involved in a bitter war of words with former chief executive Charles Green, who returned to the Glasgow club as a consultant last weekend.
Green declared that McCoist needed to win the league and a cup competition to have any chance of keeping his job, and the 50-year-old branded the Yorkshireman "an embarrassment" in reply.
The pair's continued hostilities have left Smith feeling uneasy about what he can achieve at the club, but no decision has been made on his future at this stage.