Mark Webber retires from Formula One at the end of the season and one of the most coveted drives in the sport was thought to have been between Kimi Raikkonen of Lotus and Daniel Ricciardo of Toro Rosso.
But when Alonso's name came up on Sunday Horner said: "It would be interesting. At the end of the day we have to do what is right for the team and the pairing that we put together next year will have to benefit the team.
"There are statements about Kimi and statements about Fernando but we have to make sure nothing clouds our judgment about next year. We want the two fastest drivers we can get who can work collectively together and achieve the best results for the team.
"We want to put the strongest drivers in the cars that we possibly can and Mark leaves some big shoes to fill."
There is also a suggestion that Vettel could go to Ferrari, potentially in a job swap with Alonso. He is likely to win his fourth straight title with Red Bull this year and, if he went to Maranello and won more championships there, it would confirm his reputation as one of the greatest drivers of them all.
The only trouble with that theory is that Vettel has recently extended his contract with Red Bull until the end of the 2015 season. Horner has also made it clear that there is no driver he would exchange Vettel for, and that includes Alonso.
The only solution, then, would be for the two drivers to join forces at Milton Keynes. But again that is not straightforward. Alonso wants to be top dog wherever he drives, as Lewis Hamilton and McLaren discovered in 2007. There is no way that Vettel would put up with that.
Perhaps Horner, who has a mischievous sense of fun, is merely trying to unsettle the Ferrari camp, though on recent form the Italian team are hardly a threat to his ambitions to win both world titles for the fourth consecutive year.
If Horner is spoofing, he maintained a straight face when he did so. He added: "We are in a fortunate position that there is a lot of interest in the seat for next year. We had a look at Daniel in the test, so we will take a little time over the summer and look at the options and look to make the right decision with the right pairing.
"Any conversations with any driver remain confidential. Of course, there has been quite a few drivers expressing interest in the seat. Is [Alonso] available? We are going to take a bit of time to make the right decision.
"We have some great options and we don't need to rush. There has not been any pressure that we must take a junior driver. It is a matter of fielding the best team. Of course, the junior drivers are under consideration but there is no prerequisite it has to be one of them."
There were reports in Germany's Sport Bild over the weekend that Red Bull had held talks with Alonso's manager, Luis García Abad. But the significance of this was played down by other parties.
Vettel said on Sunday: "I am sure that Fernando is a nice guy and I respect him as a driver. I would rather have Kimi. I have got to be careful what I say here but I respect him as a person and driver. He has always been very direct with me."
Alonso did not deny that his agent had been in touch with Red Bull. He had other matters to distract him, without Horner's carefully worded ambiguity.
He came a disappointing fifth in Sunday's Hungarian Grand Prix and was later fined €15,000 (£13,000) for a DRS breach.
Vettel, who was beaten into third place by Hamilton and Raikkonen, said afterwards: "It was close with Kimi. In the end we were quick in the last two corners but couldn't catch him on straights. We did what we could but surely we could have done a bit more today."
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