The superstar couple and new parents of three need to move before the end of the summer

Wanted: Los Angeles mansion fit for a king and queen. Throne room a must.

New parents of three, JAY-Z and Beyoncé have yet to find a home in Los Angeles that suits their needs and their $100 million budget, a real estate source confirms to PEOPLE. "They want to find the perfect house to buy for their family, but they haven't found it yet," the source says.

With a massive budget, and in a city of mega-mansions, the real estate options are seemingly endless. But when you're a family of global superstars, even a 9-figure price tag can be limiting. "They are absolutely on a budget. It's an insane budget, but they are sticking to it. They don't want to pay above $100 million," the source says.

And when your must-haves list includes all the amenities, privacy and security money can buy, houses that fit the bill are few and far between. "They have toured every luxurious mansion on and off the market and will continue to tour," says the source. In March, they reportedly toured the Aaron Spelling mansion. The 57,000-square-foot, French chateau-style home currently belongs to British Formula 1 heiress Petra Ecclestone and her husband, billionaire businessman James Stunt, who purchased it for $85 million in the summer of 2011, according to W Magazine.

The peripatetic family has been renting a string of luxury properties while house hunting since they made the move west from New York City in 2015 ("They are not moving from rental to rental, because they enjoy it," the source notes), but with the arrival of their twins two weeks ago and daughter Blue Ivy, 5, starting school this fall, the pressure is on more than ever to settle in. The source confirms the family's search is focused on the celeb-favorite areas of Beverly Hills, Bel Air and Holmby Hills.

Currently, the Carters are making their newest members feel at home in a stunning Malibu rental house. A real estate source confirms to PEOPLE that the couple have rented the 10-bed, 14-bath villa — which rents for $400,000 a month, fully furnished — earlier this month. The couple plan to stay at the estate through the summer while they search for a more permanent residence in Los Angeles.