Khloé Kardashian and Tristan Thompson Looking at Houses Together to 'Start Fresh': Source

Khloé Kardashian and Tristan Thompson have been touring homes together.

The Keeping Up with the Kardashians star, 36, and the Cleveland Cavaliers player, 29, have been back together since June, and a source tells PEOPLE that they've recently been looking at properties in Los Angeles.

"Despite Khloé trying to keep their relationship more private, she is very much with Tristan. And she is incredibly happy," the source says, adding that they've been looking at homes and want "to start fresh."

Last month, Thompson put his $8.5 million Los Angeles home on the market. Khloe listed her Calabasas property, asking $18.95 million, in May.

"In the past few months, Tristan has really shown Khloé that he has changed. He is an amazing dad and partner," the source adds of the pair, who are parents to 2-year-old daughter True. "Khloé was always hoping that Tristan would come around. It's been very important for her to keep her family together for True's sake."

Kardashian and Thompson called it quits last year after news broke that he hooked up with their family friend Jordyn Woods. Thompson also allegedly cheated on Kardashian in 2018 while she was pregnant with their daughter.

Despite their ups and downs over the years, the pair have always been committed to co-parenting True — and a source told PEOPLE in July that after spending time apart, they had decided to give "their relationship another try."

While Kardashian and Thompson have kept their relationship under wraps, a source recently told PEOPLE that the Good American founder is "beyond happy."

"She loves having him around. He has the best relationship with True," the source said. "And he has been amazing to Khloé too. They are very much together."

"They have been living in kind of a bubble and Khloé enjoys it," the source added.

RELATED VIDEO: Khloé Kardashian Celebrates 36th Birthday with Family — and Gets into Playful Fight with Sisters

Kardashian has previously spoken about how spending time together as a family helped the pair heal.

"So many people don't understand it, but I lead with love and we put our child first," the Good American founder told PEOPLE exclusively last month. "If you have that mindset, everything else follows easily."

"Tristan and I needed that time to heal and I needed time to go through my emotions. But now he's literally one of my best friends," she added. "A lot of that has been because of quarantine. We spend a lot of time together with no distractions, and seeing him as a dad and how helpful he is, I'm so grateful. Especially during this time because it's such an isolating time. I'm really grateful for that support and that additional help."