Inevitablya poor start to this season has led to speculation that Hamilton will grow frustrated at Mercedes after a second barren year and potentially look for an alternative home.
While the currently dominant Red Bull is obviously attractive to all drivers on the grid, Horner has stressed that both Max Verstappen and Sergio Perez are signed up for 2024.
"I think what Lewis has achieved in F1 is second to none," he said when asked about Hamilton in a Sky News business interview.
"But we're very happy with the drivers that we have, they're committed as a pair for not only this season, but the next season as well.
"So I can't see where we would be able to accommodate Lewis. But I'm sure they [Mercedes] are going to sort their issues out, and we're certainly not writing him off yet."
Mercedes boss Toto Wolff remains confident that Hamilton will stay put, despite the difficult situation at the team.
"He's a fighter and so are we," said the Austrian after Sunday's race in Jeddah.
"And if the fight is on, you stay in the fight and you don't throw the towel in, and I think that's how we all are in the team and that's why I've no reason to believe he's going to walk away from it."
Asked after qualifying in Jeddah about his future, Hamilton admitted that he's not happy at the moment, but insisted that he's fully committed to the team.
"I'm not focussed on that," he said when asked if he might look elsewhere. "I mean, I love this team, I'm so grateful for everyone that's been on the journey with me with this team.
"I don't envisage being anywhere else, and I don't see myself quitting, I don't feel like I'm a quitter.
"But I wouldn't say that it's giving me a lot. You know, I've been there and done that bought the t-shirt many times!
"But I am trying to be patient and work with the team to get us to a good place. And that's all I can say right now. I'm not going anywhere else."
