Mark Cooper and Lee Clark have both reportedly shown an interest in taking up the vacant Walsall managerial position.
Smith left Walsall in good hands at the top end of the League One table and, according to the Express & Star, plenty of names are already in the frame for the Bescot Stadium post.
Cooper, out of work since leaving Swindon Town in October, is thought to be the leading contender after guiding the Robins to the playoffs last season.
Former Blackpool boss Clark is also said to be under consideration, having previously been linked to the still-vacant position at Championship side Fulham.
It is claimed that neither manager has yet officially applied for the job, but both would be open to taking charge if approached by the Walsall hierarchy.
Club physio Jon Whitney is also among those to have been tipped with a permanent coaching role with the Saddlers, and he will continue to remain in caretaker charge until an appointment is made.