Khloe Kardashian, Tristan Thompson and True Thompson. Picture: Instagram

Khloe Kardashian and Tristan Thompson are "on the same page" when it comes to custody over their 10-month-old daughter.

The former couple recently split after Tristan was caught kissing Jordyn Woods - who was the best friend of Khloe's half-sister Kylie Jenner - at a party last month, and although things are difficult between the pair at the moment, sources say they're committed to successfully co-parenting their daughter True.

An insider told 'Entertainment Tonight': "Khloe has True for the majority of the time. Khloe's able to bring True or be with her at work, where Tristan can't. Also, True spends a lot of time with her big family and all the cousins are in LA so it makes the most sense for her to stay with Khloe.

"Khloe and Tristan may have their issues but Khloe will never deny Tristan a chance to spend time with his daughter. Things may change in the future, but for now Khloe and Tristan are on the same page with True being with Khloe for most of the time."

The 'Keeping Up with the Kardashians' star, 34, was recently said to be "figuring out" how to incorporate Tristan into their daughter's upcoming first birthday in April, without making things awkward around her family.

Another source said: "Khloé is figuring out how to get Tristan involved [in True's birthday]. She can't see how he can be around her family at a party, though. Everyone is just too upset with him."

And Khloe is thought to be particularly struggling with her sister Kim Kardashian West, who is reportedly "beyond angry" with the 27-year-old NBA star, and doesn't think she'll "keep it together" if she sees Tristan face to face.

The source added: "Kim never trusted Tristan after he cheated on Khloé right before True was born. Ever since, it's been very difficult for Kim to even tolerate Tristan. But she really tried her best because it was important for Khloé.

"[Now, Kim] says she never even wants to see Tristan. She feels there is no chance she will keep it together and not lose it on him. Kim is beyond angry with him."