Lamar Odom is "so grateful" to Khloe Kardashian.

Lamar Odom and Khloe Kardashian

Lamar Odom and Khloe Kardashian

Khloe has been caring for her estranged husband ever since he collapsed at a brothel in Nevada in October and Lamar recently moved into a rented home in the same gated community as Khloe.

A source told PEOPLE: "He can move around alone, and he can communicate much better. In the beginning, he couldn't talk at all. He knows how much Khloe has been there for him, and he is so grateful. The therapy can be incredibly frustrating and he has hard moments, but Lamar is a former athlete. He's strong. And he really wants to get better.

"Khloe continues to look after him. Khloe visits him at his house and Lamar hangs out at hers."

While Lamar, 36, is on the road to recovery, he still has a long way to go.

The insider added: "He still needs help walking. Lamar is not driving himself and instead has a driver. Whenever he leaves the house, he looks happy. He looks alert and often smiles. He is definitely looking more like the old Lamar.

"While he isn't 'back to normal' by any means, he's made so much progress."