But team owner Dietrich Mateschitz this week issued a clear denial.
Boss Horner now follows suit.
"Red Bull is a chassis manufacturer and we have no ambition to become an engine manufacturer," he told the Austrian broadcaster Servus TV.
However, the rumours are not likely to stop there. Despite Red Bull's 2016 contract, the team is not committing to running French power beyond next year.
And off the back of the very latest reports that Renault could sell its F1 facility at Viry and pull out of the sport, the new rumour is that Lotus could be considering a switch to Mercedes power for 2015.
For his part, Horner said Red Bull is pressing ahead with Renault for now.
"We have had meetings to discuss what needs to happen. At the moment there is a big difference -- Mercedes have done a great job," he said.
He said the basic problem is the interaction between Renault's combustion engine and the energy recovery systems.
"It is not working harmoniously," said Horner. "The fact is that it is not easy to recognise any progress.
"They have improved a little, but we need to know what they want to achieve.
"You have to pay Mercedes a big compliment and say they have done a great job. They started early and invested wisely," he added.