Germany's Sport Bild reported earlier that Red Bull had confirmed the meeting in the team's motor home took place at Alonso manager Luis Garcia Abad's behest.
Photos of the meeting were even published, raising the tantalising prospect of Alonso buying out the rest of his long and lucrative Ferrari deal to join arch-rival Sebastian Vettel at Red Bull in 2014.
But Auto Motor und Sport correspondent Tobias Gruner suggested the story is a false alarm, as Garcia also manages the rising Red Bull-backed junior Carlos Sainz jr.
Sainz recently tested both the Toro Rosso and the Red Bull at Silverstone, and afterwards insisted he "would not say no" if an opportunity to move into F1 arose for 2014.
"Well, maybe there is a small percentage chance," the GP3 driver told Spain's AS newspaper, "but I am 18 years old and I think if you have talent you still have to be well prepared, to mature as a driver, get experience.
"But if the opportunity came, you can't say no because it could be something that comes only once in life," added Sainz, son of the rally legend Carlos Sainz.
Curiously, when given the chance on Sunday, Red Bull's Horner did not deny the Alonso link, telling German broadcaster RTL that "there will always be speculation when we have a seat available".
Mercedes chairman Niki Lauda, however, suspects the story has been planted to destabilise Ferrari.
"It's the biggest nonsense I've ever heard, a stupid rumour," he said.
"Alonso has a contract for three more years, 2014, 15, 16 -- everybody in the paddock knows that. It's absolutely not true."
Ferrari team boss Stefano Domenicali smiled: "The psychological games are just a part of this sport."