The two-time champion Spaniard said he was not aware that his management had gone to speak to Red Bull boss Christian Horner during the Hungarian Grand Prix and blamed the rumours on the media and Formula One's four-week European summer break.
"Always with four weeks with no Formula One it's a very dangerous period for us, and the media, but hopefully we will have a quiet summer," he told reporters.
He continued in enigmatic vein when pressed for an answer by the BBC and laughed when he said he could not say if he knew if his management had spoken to Red Bull.
Meanwhile, Red Bull boss Christian Horner was also not very keen to snuff out rumours of a possible move by Alonso, according to the UK's Daily Mail newspaper.
“We are in a fortunate position that there is a lot of interest in the seat for next year," said Horner.
"We had a look at Daniel [Ricciardo] in the [Silverstone] 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," the Daily Mail quoted the Red Bull chief as saying.
“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," Horner added.
Red Bull is seeking a replacement driver for Australian pilot Mark Webber.
The 36-year-old Webber retired in June after 12 seasons at the wheel. He started 206 times and won nine races in total.