Rooney, 31, is widely expected to leave Old Trafford ahead of the 2017-18 campaign, and a number of clubs have been linked with the 119-time England international over the last couple of weeks.
Earlier this week, a clutch of leading bookmakers slashed their odds on Rooney making the move to the Britannia Stadium, but according to Scholes, the Potters are not in for the United legend.
"What I can't do is shed any light on where the rumours have come from," the Stoke Sentinel quotes Scholes as saying.
"That happens at this time of year. We have some speculation, some of it is based upon some truth, no smoke without fire, but other times you get wild speculation, and the Wayne Rooney one falls into the latter category.
"Wayne Rooney has been one of the best players of his generation. He has been, and still is, a great football player. But there have been no conversations whatsoever about Wayne Rooney coming to Stoke."
Rooney, who scored five times in 25 Premier League appearances during the 2016-17 campaign, still has one year remaining on his £300,000-a-week contract at Old Trafford.