It's no secret that former President Barack Obama and his family love Martha's Vineyard, having vacationed on the idyllic Massachusetts island seven out of the eight summers they were in the White House, as well as this August. And rumors are now flying that they're looking to purchase property in the area.

Local real estate agents are tight-lipped on the reports that the Obamas are house-hunting, since part of the charm of this island is that despite its popularity, VIPs can still get plenty of privacy. That's why it's a magnet for celebs—including Bill Clinton, Larry David, Alan Dershowitz, and David Letterman—some of whom can be frequently sighted at low-key hotspots like the front porch of the Chilmark General Store. According to anonymous sources cited in the Boston Globe, the Obamas are shopping for homes or land lots in the northern, less populated regions of Aquinnah, Chilmark, and West Tisbury.

In particular, the Globe suggests the former president might be eyeing two oceanfront properties in Aquinnah that were once part of the 377-acre Red Gate Farm owned by Jacqueline Kennedy Onassis, who passed this property down to Caroline Kennedy and her husband, Edwin Schlossberg. They later subdivided it into these two parcels.

One parcel is 75 acres at 8 Red Gate Farm Road, for sale at $15 million; it's pictured below.

8 Red Gate Farm Road realtor.com

The second, seen below, is a 40-acre parcel at 6 Red Gate Farm Road, for sale at $12 million. Both are listed with Hancock Real Estate in Chilmark (which refused to comment when we called).

6 Red Gate Farm Road

Granted, even without a fabulous mansion on the premises, it's clear that either (or both!) of these properties would offer the Obamas a slice of heaven on earth.

"Both lots are stunning," says Joy Cifuni, a real estate agent in Cape Cod, MA, at Keller Williams. "If I had to choose, I would pick the one for $15 million, because of the extra acres."

While comps in this price range are tough to come by, a 106-acre lot at 3 Red Gate Farm Road sold in 2012 and is currently valued at $12,685,000. So, given that these lots for sale are in the same price range (or higher) but offer far less land, you've gotta wonder: Are they overpriced? Possibly, considering the length of time they've been lingering unsold.

"Both pieces of land have been on the market for 83 days," points out Cifuni. This could spell an opportunity for the Obamas, should they decide to make an offer.

"Personally, I would deduct 10% from asking," says Cifuni.

Those savings could come in handy, since the Obamas will have to build a home from scratch, which is no small undertaking on this island south of Cape Cod.

"Being on the ocean creates its own challenges, like steps constantly washing out, erosion of land, and painting needing to be done more consistently because of salt," says Cifuni. "Picking the right builder is the most important step they could possibly make."

Other experts agree that building the perfect house could bring the former first family a ton of headaches.

"As good as a builder may be, problems always arise, causing delays," says Denise Supplee, a property management specialist at SparkRental. "And although the Obamas do have a political advantage, there is much to deal with in zoning, licensing, permits, and ground preparation."

"The Obamas need to check all permits, and [see] if their land can be subdivided, and if it's on Wampanoag land," says Julianne Kavoussi, who has owned a home in the Edgartown part of the Vineyard for 20 years. The Wampanoag are Native American people who, she says, own a good portion of Aquinnah.

Nonetheless, this land is bound to be a great investment.

"Oceanfront property here holds its value," says Cifuni. "It's the first to come up in price from a declining market, and the last to go down in a declining market."

In other words, if these rumors are to be believed, the Obamas have picked a great place to put down some roots. Lobster roll, anyone?