"You have to have other irons in the fire because if you're chasing a quality player you can never be sure you have them until they sign on the dotted line," he said.
Posh chairman Darragh MacAnthony has promised Johnson the funds to mount a promotion push next season.
The former Bristol City boss wants to seal his first signings by the middle of June at the very latest.
"We've made two offers and they're mulling over the terms at the moment so it should be done soon," he said.
"We're ideally looking for six or seven players and I'm looking at strengthening in most positions."
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