It was suggested that the 25-year-old Bosnian was set to link up with the Reds for pre-season training ahead of the new Premier League campaign and he was quoted as saying: "I want to start preparing on July 10, with all the players of Liverpool."
However, Stoke chief executive Tony Scholes has moved quickly to say there is no truth to the report.
He told the club's official website: "Asmir's agent rang me as soon as these stories surfaced. He assures me that Asmir doesn't know the Bosnian journalist and has certainly never spoken to him.
"It's complete fabrication and unfortunately it has been picked up by a paper in this country.
"It's inevitable when a manager parts company with a club that there's a period of uncertainty and erroneous newspaper reports certainly don't help matters."
Begovic said earlier this season that he expected to be sold after Stoke signed England goalkeeper Jack Butland in the January transfer window before loaning him back to Birmingham City.