Alleged inside sources told BBC Sport that the Spaniard attempted to jump ship over the summer, only for the rival team to choose Daniel Ricciardo instead.
However, Alonso has insisted that there is no truth to the reports and expressed his desire to extend his stay at Ferrari beyond his current contract.
"It was only rumours," he said. "A lot of rumours - about Red Bull, about a sabbatical year. So many rumours.
"I have three and a half more years with Ferrari, which I intend to respect and hopefully increase a little."
Alonso's current deal with Ferrari expires at the end of 2016.