The Cobblers have already released six players and Adebayo Akinfenwa and Andy Holt have rejected contract offers.
Cardoza told BBC Radio Northampton: "We've lost a couple of the bigger earners and the manager has the opportunity to rebuild.
"We've got five to seven players to bring in. I think we'll still be adding in July and maybe August."
He continued: "I think we need a striker, a centre half, a right back and a central midfielder.
"We may need a left winger, depending on what happens with Liam Davis, and possibly someone on the right wing as well."
Cardoza has praised his manager Ian Sampson for the decision to set players a deadline on whether or not they were signing new deals at the club.
Top scorer Akinfenwa failed to make a decision by the deadline, and has left the club.
"He was offered a substantial increase on what he was already earning," Cardoza said.
"We can concentrate on bringing different targets in now. I think it was an extremely good move by the manager and a brave one."
And the chairman is confident that if the signings are forthcoming, Northampton will be challenging for top honours in 2010/11.
"It's still too early to say because we haven't signed our players, and nor have the other teams," he said.
"But we're one of the bigger clubs, with one of the biggest wage bills, and we should be up there.
"If we'd have started last season better, we'd be talking about League One now, so it's important we get off to a good start."
Source: BBC Sport
Source: BBC Sport