The American administrator, elected to his new position last September, said that the list of unfinished items in Rio includes adding another layer of surfacing to the Summer Games' hard courts.
Fixing the stadium lights is another objective, along with installing stands for spectators at smaller courts and "making sure the surroundings are the way we want them to be."
"By the time the Opening Ceremonies are completed - we should be fine." Haggerty told Associated Press.
The tennis competition is scheduled to begin on the morning of Aug. 6, the day after the opening of the Summer Games.
Haggerty said he visited Brazil about a month ago and there was "work to be done - probably all venues would say the same thing."
"It's the sort of thing that, when you don't see the stands yet put in, you worry," he said.
In January, Rio de Janeiro's Mayor rescinded the contract for the tennis centre, which is located in the Olympic Park, because the project was moving too slowly.
A spokesman said the local Organising Committee was confident the work would be completed when it had to be.
Haggerty said the ITF is keeping an eye on things, with visits "down there all the time," including an upcoming trip by the governing body's secretary general.
"We want to make sure the athletes' experience is the best it can be," Haggerty said.
"They'll leave Wimbledon [in July]; they've been at the French Open.
There are expectations...so we want to make sure the experience they have is the world-class experience that they should have.
"So we're paying attention to details and trying to see what we can do there."
Haggerty’s warning over Rio comes just four days after Brian Cookson, President of the International Cycling Federation (UCI) said the governing body was “extremely concerned” about delays to the construction of the Rio 2016 velodrome.