The Saddlers' need for fresh faces has been emphasised by a four-game winless run and a growing list of absentees.
Defenders Stephen Ward and Rollin Menayese were injured and sent off respectively in a 2-0 loss to Exeter City on Saturday, meaning they will miss the game against the Bantams.
When asked if any business will be done before the game, Walsall chief Taylor – whose side are now 17th in League Two – said: "I hope so. I'm an optimist, and I hope so.
"We're working very, very, very hard.
"There's been lots of phone calls and lots of conversations with lots of people. We're working extremely hard."
He added: "We're well aware in terms of the positions we need to strengthen.
"We're doing everything we possibly can to try and have some new additions in the group for Tuesday."