During the last campaign, Harrison netted 10 goals in 36 appearances and it has led to greater attention in English football, with the winger being handed his England Under-21 debut late last year.
The 21-year-old told The Independent: "As to the Stoke City rumours, nothing is official yet. I'm still a New York City player right now and that's where my mind is at.
"Everyone dreams of playing in the top leagues in Europe and the Premier League is obviously up there. Growing up in England, it's always been a dream of mine to play in the Prem. But as of right now, I'm still a New York City player.
"I just leave it all to my agent. I don't like to think too much about that stuff or get caught up in it."
Leicester City have also been linked with Harrison in the past.