Scouts from 17 Premier League clubs, including Tottenham, watched Clayton score on his first senior start against Macclesfield on Wednesday.
But Gradi told BBC Radio Stoke that he was disappointed to see newspaper reports linking the 17-year-old with a move to White Hart Lane.
"It doesn't do anyone any good, it raises the expectation level," he said.
"There's a high level of expectation placed on these kids. For instance, there's a line in the newspaper this morning linking Max with Tottenham.
"His parents are terrific and that's why he's handling it very well, but sometimes the parents can get carried away and they put great expectation on their kids.
"With the great rewards that there are now for players who make it to the top, there's definitely more pressure than there used to be."