The Saddlers have been open in their pursuit of another attacker – technical director Jamie Fullarton having visited an unnamed player who several clubs are chasing last week.
And Taylor, whose side are hosting Forest Green Rovers tomorrow afternoon, admits he would like one or two fresh faces before the end of the window, on top of the 12 brought in so far this summer.
"Football is a difficult game to predict. For me to sit here and say I'd like two in or one in, that's the truth," he said.
"But how likely that is to happen, I don't know.
"I'm really pleased with where the group are and how they're performing. I'm enjoying the dynamic and the relationships they're building.
"So, if we do add new players, they have to be right players and the right people.
"The last thing I'd want would be to change the dynamic of the group through the wrong signing.
"We're working as hard as we possibly can – as are probably every club up and down the country – to try to make sure that the squad is as complete as it can be by the end of the transfer window."
Taylor admits the market is now moving a bit slower than it was earlier this summer.
Walsall, though, remain hopeful of securing their targets.
"I'm very hopeful. We are scouring. We've got our targets," added Taylor.
"The beginning of the window was quite frantic, but now lots of clubs are kind of seeing where the land lies.
"They're seeing there's a player they don't need or a player they do need.
"I expect it to open up and for us to have one, maybe two, in before the end of the window.
"What I will stress is that they'll be the right people."