The likes of Liverpool, Juventus and Real Madrid have all been credited with an interest in the highly-rated centre-back in recent weeks.
Shawcross has established himself as one of the best young defenders in the country after catching the eye at The Brit over the last couple of seasons.
Scholes insists Shawcross, who signed a new deal to keep him at the club until 2014 last season, is going nowhere and remains a big part of the plans for the future.
"I had heard about the Liverpool story, but not the Juventus one. I'm sure Ryan will smile about it," Scholes told The Sentinel.
"There is no truth in the rumours, but the speculation shows how far Ryan has come in his time here and how he is turning into one of the best young centre-backs in the country."