Could little Blue Ivy make her first appearance in the Hamptons next week? Sources tell us the 6-month-old’s parents, Jay-Z and Beyoncé, are renting a 31,000-square-foot home in Bridgehampton — known as the Sandcastle — for a staggering $400,000 for August.

The 11-acre property on Halsey Lane was built by Hamptons super-developer Joe Farrell. It’s currently on the market for $43.5 million.

The sprawling estate is fit for the king and queen of Hip-Hop, lavishly equipped with a two-lane bowling alley, virtual golf, skateboard half-pipe, a rock-climbing wall, a full bar and recording studio.

It also boasts a 60-foot heated pool with an underwater stereo system, a tennis court, a spa facility with gym and a combination squash, racquetball and basketball court with moving walls and retractable hoop — plus an eight-car garage.

In addition to a 2,800-square-foot master suite, the place includes a separate two-bedroom apartment. The estate also has what’s called a “children’s performing area,” according to the listing on Corcoran.com — perfect for baby Ivy.

After 18 months of construction, Farrell moved his own family into the house in 2009 but has since rented it out for a short time each summer at record-breaking prices. The Jonas Brothers were rumored to have been interested in it but settled on another Hamptons rental instead.

In 2010, Sandcastle was famously rented for $500,000 for two weeks by Tampa, Fla., single mother Cheryl Mercuris, a direct-marketing whiz who wanted to plant herself in the Hamptons in order to bag a billionaire mate. She didn’t find the man, but she had some great parties, we are told.

She rented the palatial home again the following summer for the month of July but declined to reveal how much she paid.

Reps for Jay-Z and Beyoncé, Farrell Building Company and Corcoran didn’t get back to us.