The Hornets made Gray their record transfer earlier this week, with Burnley unable to tempt him to stay put.
Gray has only ever represented his country at England C level but the 26-year-old is still dreaming of a call-up to the national team.
He scored 32 goals in 73 games for the Clarets but Gray admits his current form is not worthy of a place in the England squad.
However, the former Brentford man admits he is still dreaming of a place in Gareth Southgate's squad.
He told reporters: "That is an ambition of mine ever since I played for England C. I have got to prove myself here yet and score goals and then go from there.
"Am I good enough? Not at the minute, if I am honest. I feel like I have got the potential as long as I keep improving.
"I would like to keep that [raw talent] in me. That is the lion in me that keeps me going. But I still need to polish up on a few things to get the call-up.”