"I wouldn't rule anything out at the moment," the Briton told reporters in a teasing, cat-and-mouse briefing in Red Bull's double-decked hospitality unit at the Belgian Grand Prix.
"As far as I'm aware he hasn't signed a contract with anyone yet."
Pressed on whether the 2007 champion for Ferrari who is currently second in the overall standings with Lotus, was definitely off Red Bull's list, Horner replied: "That's up to him.
"I think Kimi's manager's ruled him out...I've only seen what you've seen, only read what you've written."
Horner said the team, winners of both titles for the past three years, had not yet decided who would partner Germany's triple champion Sebastian Vettel - despite reports that Australian Daniel Ricciardo had been given the nod.
The most coveted seat on the grid has been available since Australian veteran Mark Webber announced he was leaving at the end of the season for a new career in Le Mans sportscars with Porsche.
Raikkonen and Ricciardo had been presented as the two contenders and the duel appeared resolved when the Finn's manager Steve Robertson told autosport.com this week that "Kimi will not be driving for Red Bull in 2014".
However Ricciardo said he had been told nothing and felt the seat was still "up for grabs".
Asked whether he was taking Robertson's comments with a 'pinch of salt', Horner would not be drawn. "Wait and see," he said.
In comments that left plenty of unanswered questions, and were sure to stoke paddock speculation further about other leading drivers, he also indicated more names were under consideration.
"You have to make sure you consider all the options and there's more options than you would possibly think," said Horner.
"There's been quite a lot of interest. So we'll just take the time. It's not going to be much longer I would have thought. By Monza (on Sept. 8) or shortly after we should be clear."
Asked whether a new contender had emerged, Horner replied: "You'd be surprised at the approaches that we've had...I don't want to compromise any discussions that may or may not be happening."
Horner said any suggestion that Vettel had vetoed Raikkonen joining the team was 'absolute rubbish' and the German had no such influence.
Raikkonen has also been linked to a possible return to Ferrari, with Brazilian Felipe Massa regularly tipped to be dropped, but there has also been speculation about Fernando Alonso's intentions.
The Spaniard, clear number one at Ferrari and with a contract to the end of 2016, was caught in a flurry of speculation in Hungary last month when his manager was seen entering the Red Bull motorhome for talks with Horner.
The manager said he had been discussing young Spanish prospect Carlos Sainz junior.
Jenson Button, the 2009 champion with Brawn GP, was asked on Thursday about his contract with McLaren as the rumour mill began to suggest he could be a target for Ferrari.
The Briton said he intended to stay with McLaren although he had yet to sign a contract.
All Formula One contracts usually contain performance clauses and options triggered at a given point in the season, which could also explain Red Bull's delay in making a decision.
"I don't know the details of everybody's contract," said Horner, when asked if that was a factor.
"There is no transfer window in Formula One," he said. "We're not obliged to make a decision until we choose to. And we want to make sure we make the right decision and we'll take the time that we feel appropriate to make that decision."