Each of the country's six host stadiums for next month's Confederations Cup - considered a dry run for the World Cup - overshot their original deadlines of December 2012.
But Itaquerao, which will stage six World Cup matches, including the tournament opener and one of the semifinals, has caused the greatest concern for FIFA.
Developer Odebrecht is still awaiting a promised $200 million loan from state-run banks it says is needed to step up the pace of works.
Valcke will visit Rio de Janeiro's Maracana stadium on Wednesday, which will be officially reopened on June 2 for an international friendly between Brazil and England.