The Lions are searching for a new boss since sacking Ian Holloway in March, with Neil Harris in caretaker charge.
They are set to be relegated from the Championship and are four points from safety with just two games left.
Smith is the fourth longest-serving manager in the country, having been appointed by the Saddlers in January 2011 and has turned them around having taken over when they were bottom of League One.
They reached Wembley for the first time in their history last month, losing the Johnstone’s Paint Trophy final 2-0 to Bristol City, and Smith has dismissed speculation over the Lions role.
He told the Walsall Advertiser: “It’s the first I’ve heard of it, I’ve not heard anything and I’ve got a job to do here.”
Meanwhile, Smith also confirmed he is hoping to tie down Paul Downing and Kieron Morris to new deals this week and added: “There are a lot more talks ongoing too.
“We’re still speaking with Richard O’Donnell, while Adam and James Chambers, James O’Connor and Ben Purkiss are out of contract too.
“We have done very well as a team defensively and talks will be coming with those players pretty soon. I am just waiting to get the budget for next season.”