Horner told the Daily Mail newspaper there had been "several conversations over the years" about Hamilton joining the team who are currently dominant with triple world champion Max Verstappen.
"They have reached out a few times. Most recently, earlier in the year, there was an inquiry about whether there would be any interest," said the team boss.
Hamilton, whose contract to the end of 2025 was announced in August, told reporters at the season-ending Abu Dhabi Grand Prix on Thursday that nobody from his management had spoken to Horner.
He said Horner had messaged him, however, on an old phone he had left at home.
"I switched it on and obviously hundreds of messages came through and I realised there was one from Christian to get together and have a chat at the end of the season," he said.
"I just replied to him on my new phone. It was after a weekend. It was quite late on that I found the message. It was from earlier on in the year. So, it was like months later."
Hamilton also suggested some people liked to drop his name into conversation to get attention if they were "a little bit lonely".
"I think he's just stirring things," he had told Sky Sports television earlier.
"You know Christian. He loves that kind of stuff."
Hamilton said he would be "more than happy" to race Verstappen in an equal car and any driver would love to drive "for such a great group of people" but it was not his personal dream.
"I think moving from a car that's not so great to a winning car, from my perspective that's not a dream. The dream is always to start like where we kind of are and build up to then winning. That's why I've stayed with Mercedes," he said.
Mercedes won eight constructors' titles in a row from 2014-21 but are fighting Ferrari to be best of the rest this season. Verstappen has won 18 of 21 races so far and Red Bull has won all but one.
"SERIOUS TALKS"
Horner told the Daily Mail that Hamilton, who has not won a race since 2021, also held talks with Ferrari chairman John Elkann earlier in the year.
"I think there were serious talks. It was around Monaco (in May). There were definitely conversations, perhaps with (Ferrari team boss Fred) Vasseur, too. But certainly with Elkann," he said.
Hamilton, who has said he sees himself at Mercedes "until my last days", denied the Ferrari speculation at the time.
He also told reporters in May that his management team were handling contract talks.
It is not unusual for a driver's representative to investigate other possibilities at a time of contract negotiations.
Verstappen asked in an FIA press conference whether he would have welcomed Hamilton as his teammate, and saw little point in fuelling the discussion.
"There's no point to make up stories 'if, if'. It's not happening," said the Dutchman. "I wouldn't mind, it doesn't matter."
