The 18-year-old German has yet to appear for County's senior side, but his displays at youth level have attracted a host of Premier League interest.
"Man United have been looking at him for a long time. There were also scouts from Man City and Tottenham at our youth game against Doncaster last week and Arsenal watched him when he was out on loan at Lewes," Leonard told the Nottingham Post.
"He's as good as any young goalkeeper I have seen and I wouldn't be surprised if any of the big clubs did want him. He can go all the way if he keeps working as hard as he is now. He has got so much potential."
Leonard first scouted Spiess in a centre of excellence in Duabi.