Wrexham left back Cacace has been sidelined since February with a hamstring problem but is back in full training, Bazeley told New Zealand news website Stuff on Friday.
"He was close to being involved against Oxford United," Bazeley said of the midweek match. "He feels good. He’s hoping he’ll be involved this weekend."
Boxall, sidelined for more than a month with an adductor strain, was being managed cautiously by U.S. club Minnesota United but was fit enough to play again.
"If this was the World Cup now, he would be available for selection," he added.
Bazeley was also glad to see captain Chris Wood, the nation's record scorer, back in action for Nottingham Forest after an injury scare, while several other players are nearing a return.
Midfielder Sarpreet Singh is close to returning from a knee injury for A-League side Wellington Phoenix while defenders Francis de Vries and Nando Pijnaker are expected to be a part of Auckland FC's finals campaign.
Veteran winger Kosta Barbarouses missed Western Sydney Wanderers' loss to Wellington last weekend with a calf problem but should be fit for the World Cup.
The All Whites, returning to the World Cup for the first time since 2010, kick off their campaign on June 15 against Iran in Los Angeles before facing Egypt and Belgium in their other Group G matches.
Bazeley said he was on tenterhooks watching players in their club matches seven weeks out from the finals.
"It's a worrying time, every time players are playing now," he said.
"We're going to be living like that for the next month, until we get to the World Cup."
