Parkinson said plans to strengthen his squad started immediately after his side's League Two play-off final win over Northampton, but is prepared to wait in order to bring in the right players.
"It's very easy to sign players at this stage of the summer, but they're often not quite the sort of quality that you need," he told the club's official website.
"We're competing with other clubs for players so that means we have to wait and be patient."
He added: "There is a budget in place we have to work with, and I don't want to spend it all too early and miss out on some of my preferred signings just because we weren't patient enough to wait for their signature.
"We've got some offers out there on the table to players and we've tested the water with a few others.
"I should still imagine, however, it will take a couple more weeks."