Bad weather has routinely played havoc with the US Open schedule in recent years with the men's final being pushed to Monday from Sunday for each of the past five years.
"Obviously it's going to be great," world number one Serena Williams, a four-times US Open champion, said after reaching the last 16 at the Western and Southern Open in Cincinnati.
"It's going to take a really long time. They have a long term plan, super long term, and it's not going to happen next year or the year after.
"It's good to know that they're going for it."
Centre courts at Wimbledon and the Australian Open have retractable roofs, while plans to cover the main court at the French Open had left the US Open as the lone holdout.
Reigning men's US Open champion Andy Murray lamented that some of the character and romance of the four Grand Slams was slowly being removed with the elements no longer factoring into the play.
"For TV and stuff, it's fantastic, always good that you know matches are going to get finished," Murray said after reaching the third round in Cincinnati.
"I do feel like sometimes it (weather) is kind of part of the Slams a little bit. I don't necessarily miss being rained off but rain delays and stuff, it used to be part of it; whereas now that's kind of going away gradually.
"I don't particularly like going from indoors to outdoors to indoors but it's good for TV and good for fans that are watching."
Opened in 1997, the Arthur Ashe stadium has a capacity of 22,500, making it by far the world's largest tennis stadium.
The scale of the arena had been one of the main logistical challenges that emerged from previous feasibility studies with the United States Tennis Association previously saying a roof would be "technically complex and financially challenging."
This year's US Open, which runs August 26 to September 9, has a Monday finish included as the official final day for the first time.
"Over a two week period in the summer, end of summer, beginning of fall, chances are it's going to rain at least a little bit," said the top ranked American man John Isner.
"Maybe I can still be playing when that roof is up.
"That would be pretty neat. I can't imagine the expense of it and how they're going to do it but it will be really cool.
The answers will come on Thursday when the USTA will hold a news conference to detail the plans, which are part of a major overhaul of the venue, including the creation of two new stadiums at the Billie Jean King National Tennis Center.