In a new trailer for The Kardashians, which is set to air on 14 April, the reality TV star is seen attending several fertility clinic appointments with Barker.
“Travis and I want to have a baby,” Kardashian, 42, tells the cameras. In one short clip, she is seen lying in a hospital bed while Barker holds her hand.
In another, a doctor is heard telling her to “put the sample in a cup”.
Both Kardashian and Barker already have children from their previous relationships.
Kardashian shares and co-parents three children – Mason, 12, Penelope, 9, and Reign, 7 – with her former partner, Scott Disick.
Barker has two children from his previous marriage to Shanna Moakler: Alabama, 16, and Landon, 18.
The show will also cover the Blink-182 drummer’s lavish marriage proposal to Kardashian, which took place last October.
The trailer shows the moment Barker got down on one knee on a beach in California, and later sees them kiss in front of their families as they celebrate their engagement.
In a recent interview with Variety, the Poosh founder said her relationship with Barker will not be a main storyline of the upcoming Hulu show.
Her tumultuous relationship with Disick was well-documented in the earlier seasons of Keeping Up With The Kardashians.
“I definitely hold my relationship really close,” she said of her and Barker.
“It’s so sacred to me and I am very protective of it. I think I’ve learned a lot of lessons. There is a lot of us on there, and we’ve had such a good time doing it because we have such a good time when we’re together, but I definitely want to protect it as much as I can.”
While Kardashian admitted that filming is “not his thing”, she said Barker has no objections to being on camera.
“He obviously has a full-time job and a full career, so it’s not his thing, but I think he’s happy to, and we have had so much fun while we’ve been filming certain things that we’re doing, so I’ll just invite the producers to come along,” she said.