Rotherham United are searching for a new manager following the departure of Steve Evans last week after just over three years in charge of the Millers.
As revealed by HITC Sport, former Leeds United boss Neil Redfearn is the leading contender for the Rotherham job and his availability, in that he won't cost any compensation, makes him an attractive proposition.
However, Rotherham are keen to speak to all of their targets before they make their decision on who will replace Evans, and Smith is thought to figure prominently on their shortlist.
Smith is regarded as one of the best young managers in the Football League and he has guided Walsall to a superb start in League One this season, with the Saddlers currently sitting in second spot in the table.
Rotherham have expressed a desire to speak to Smith over the managerial vacancy at the New York Stadium, but Walsall have flatly turned the approach as they have no desire to lose their manager.