The Saddlers have stepped up the search for a permanent boss after Saturday's 2-0 home defeat at the hands of Oldham left them sitting in 21st place in League One.
However Ternent has denied rumours in the weekend press that he is the man for the job.
He has been out of work since leaving Gillingham at the end of last season.
A club spokesman said: "We have interviewed a number of candidates, but the chairman is keen not to rush into an appointment."