The reigning Italian champions are without a recognized number nine for the start of 2020-21 as Gonzalo Higuain closes in on a switch to Inter Miami.
Edin Dzeko has also been linked but was part of Roma's starting line-up for Saturday's friendly win over Cagliari.
With the window open for another three weeks, Pirlo admits the troublesome position needs to be filled.
"I need the striker as soon as possible," he told Sky Sport Italia. "But the market is long. There will be time to be able to work until October 4."
Juventus kicked off their shortened pre-season program with a 5-0 win over Novara on Saturday, with Cristiano Ronaldo opening the scoring against the Serie C side.
Ronaldo also struck twice in Portugal's 2-0 win over Sweden on September 8 after recovering from a toe injury and Pirlo is happy with the forward's fitness.
"Cristiano is fine," Pirlo said. "He proved it with Portugal and also today."
Aaron Ramsey, Marko Pjaca and a brace by Manolo Portanova gave Juve a commanding win in their friendly, which Pirlo used to experiment with various formations.
"In the first half, we played with four at the back, which becomes three in the different phases," said Pirlo, who was appointed as Maurizio Sarri's successor in August.
"In the second half, we stayed with three, preparing different solutions."