Reality TV star Khloe Kardashian is confident her estranged husband Lamar Odom is "doing amazing" as he continues to recover from a suspected drug overdose.

The former basketball player has been hospitalised in Los Angeles since October (15) when he was found unconscious in a Las Vegas brothel, and reportedly suffered a series of strokes as well as problems with organs including his kidneys.

His condition has improved over the past three months, but a full recovery is expected to take more than a year as he undergoes physical and mental rehabilitation.

Khloe, who split from Lamar in 2013, was asked for an update on his recovery during a question-and-answer session in Pasadena, California on Wednesday (06Jan16) for her new talk show Kocktails with Khloe.

She replied, "It's not my story to tell, I want to respect that and I want him to be able to tell that story... I'm just there to support and care for him, but he's doing amazing and I'm so proud of the strength that he has to fight this battle that's his battle, and I'm so grateful for everybody's love and concern because I do think it's coming from a good place."

She also told the audience at the 2016 Television Critics Association Press Tour that she will include talk about Lamar in her new TV show, adding, "Definitely, because it's such a conversational show and I'm kind of bantering with my friends. It does come up because it's my life. It's happened when we've been doing test shows. It's happened that I've just been very conversational with that, but I'm not going to force it. It's been flowing."

Lamar's son posted a photograph of his father online over the festive holidays (Dec15) to prove he is making a good recovery.