Kieffer Moore has led the line in Wrexham’s two Championship fixtures with Sam Smith coming off the bench.
Williamson confirmed that they are working to give Parkinson more firepower.
He said: “There are probably 72 other clubs looking for the same shiny new striker, right?
“That’s the challenging one to find – the striker who is great with his feet, great with his head, great at hold-up play, great at finishing, is 6ft5ins and wants to move to Wrexham.
“That’s your £40m striker right there, but we have two great strikers on the pitch right now.
“We are comfortable with those two guys up top and what we need to just add is quality with a couple of different pieces on the pitch to give them the opportunity to score more goals.”
Wrexham host Birmingham on Friday, 28 August (20:00 BST) and travel to Millwall the day after the transfer window shuts.