"Kendall and Ben have spent the past few days together in L.A. They do seem a bit more serious," a source tells PEOPLE

Kendall Jenner‘s romance with Ben Simmons is continuing to heat up under the summer sun.

In the time since the Keeping Up with the Kardashians star was first rumored to be dating the NBA player at the end of May, the new couple has been spending more time together in her hometown of Los Angeles — including at Simmons’ swanky new pad.

Despite reports that they’re living together, a source tells PEOPLE, “Ben is renting the house. Kendall is not on the lease. It’s a gorgeous house, so it makes sense that she wants to stay over as much as possible.”

“Kendall and Ben have spent the past few days together in L.A,” the source adds about the supermodel and athlete. “They do seem a bit more serious.”

On Thursday, the pair enjoyed lunch at South Beverly Grill in Beverly Hills and then went shopping at Neiman Marcus.

“They seem to have a great time together. Kendall looks happy with Ben,” a second source says. “You can tell she is enjoying her summer.”

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A day before their lunch and shopping date in Beverly Hills, the duo was spotted Wednesday in L.A., where they were all smiles as they made a stop at a gas station.

At one point, Simmons even leaned in for a sweet kiss.

Jenner, 22, and Simmons, 21, have yet to comment on their relationship status,.

Just last week, the pair was spotted partying at Hyde nightclub in Hollywood after grabbing dinner at celebrity hotspot Craig’s earlier in the evening.

On May 30, they were spotted hitting up the Nice Guy in West Hollywood. Though they arrived separately and exited through different doors, Jenner and the Philadelphia 76ers player got in the same SUV at the end of the night, according to video obtained by TMZ. The Blast also obtained video of the couple entering the Waldorf Astoria Hotel in Beverly Hills around 2 a.m.

Still, a source recently told PEOPLE that Jenner is enjoying the single life and isn’t looking for a “serious relationship” right now.

“Kendall is having fun. She doesn’t want a serious relationship and is just enjoying being single,” the source said. “She feels that whenever she has been serious about guys in the past, it’s kind of a mess and doesn’t work out. She invested time in the relationship with Blake Griffin. She isn’t planning on doing the same right now.”