The former Hollyoaks actor explained that the role would be the "most challenging", and that it is a big "ambition" for him in the future.
"A dream acting role, and the most challenging role for me, is Hamlet," he told PA.
"If I could get the chance to play Hamlet in a production, I think all my dreams would come true. That is definitely an ambition of mine at some point."
Vye filmed his final scenes as policeman Ethan Scott for Hollyoaks last week, and added that he found his stint on the soap "fun". However, he said that he is now looking forward to doing more theatre work.
"I started off joining a local youth theatre when I was 11. It gave me an incredible foundation and grounding and taught me everything about different aspects of acting and performance.
"I did TV work when I was younger until I trained at the Royal Academy of Art. I'll do anything I can get my hands on really - I've done everything from theatre, TV and film and I'm passionate about all mediums. Theatre is one of my first loves.
"It's just so immediate and you can seek out the audience. I'd definitely like to do more of that in the future. I like doing it all. If I can manage to do it, then I will."
Vye recently said it was another ambition of his to play a television cop before starring in Hollyoaks.
> Hollyoaks star Craig Vye talks Ethan exit: 'I had an amazing year'