Grayson believes that the Yorkshire club will continue to progress after they narrowly missed out on the play-offs last season, finishing seventh.
“Finishing in the top six is a difficult ask for everybody and only six teams can do it but we’ve got high expectancy levels here," said the Leeds boss.
“The remit of the manager is to keep the club progressing season by season and we’ve done that since I came here two and a half years ago.
“This is a proper football club and eventually it’ll be back in the Premier League but there’s no reason why we can’t do that this season. We’re certainly capable.
“A host of teams will think they can get promoted and we like to think we fall into that category."
Leeds begin their Championship campaign on Saturday afternoon, when they take on Southampton at the St Mary's Stadium.