Horner admits he was not approached by Hamilton
He also made clear the only contact he received had come from his father Anthony Hamilton, who ended his management of his son's racing career in 2010.
Speaking to reporters during a news conference at the Abu Dhabi Grand Prix, Horner admitted he had had no "serious discussion" with Hamilton.
This came after Horner had told the Daily Mail newspaper that there had been "an inquiry" from Hamilton about the possibility of driving for Red Bull next season, before he signed a two-year extension to his contract with Mercedes.
Hamilton on Thursday denied these claims, suggesting Horner was "stirring things up".
"I've not approached Christian. I haven't spoken to Christian for years," he said.
"I've checked with everyone and no one from my team has reached out to him. There aren't any confidential discussions. You know Christian... he loves that kind of stuff."
On Friday, Horner said: "It's remarkable how much traction this has got so thank you to the Daily Mail for going exclusively large on this item.
"I mean, it's a question of 'He said, she said, who said, what said'... It's entirely normal for drivers, drivers' representatives and drivers' parents to have different conversations during the course of the year."
Hamilton has driven for Mercedes since joining from McLaren for the 2013 season, winning six drivers' world titles with the team.
"And look, you know, we haven't had any serious discussion with Lewis. There was never a seat available," added Horner.
"I've known Anthony Hamilton for many years. He's a good guy. He's a proud racing father and inevitably, when drivers go through tough spots -- and let's face it, Lewis hasn't won a Grand Prix for two years -- it's inevitable questions will be asked up and down the paddock.
"But there was never any engagement and I don't know who represents who or what, but with the same surname, you would think they were reasonably close...
"It's difficult to say, but other than pleasantries, there was no specific 'Can I drive for Red Bull next year?'."
'Doubt I was only one'
He said he did not think Mercedes would be surprised to learn that anyone from Hamilton's team made contact with Red Bull.
"He's the most successful driver of all time and hasn't won a Grand Prix since 2021 so you haven't got to be a rocket scientist to work that out.
"And I doubt that I was the only one that there was an inquiry made to... Now, what the dynamics are within any given relationship? I don't know... I'm not privy to that, but inevitably questions are going to be asked.
"There's not really much more to say. A lot has been made of something fairly innocuous."
Horner's final comments may have been a response to Hamilton's summary on Thursday when the Briton said: "If you really think about it, there are a lot of people here who really like to drop my name in conversations because they know it is going to make waves.
"And if you are a little bit lonely and are not getting much attention that is the perfect thing to do -- just mention my name."
Hamilton has consistently pledged his loyalty and support to Mercedes since controversially missing out on his eighth world title to Max Verstappen in Abu Dhabi two years ago.