The 19-year-old scored 26 points for Quins - a personal record - in the 51-23 victory over Sale Sharks on Saturday.
Smith only made his professional debut for the Premiership outfit at the start of 2017-18 and his performances have remained consistent throughout.
The number 10, who has represented England at under-18 and under-20 level, has trained with the senior side.
His display against the Sharks has prompted talk of a fresh call-up and although he insists his main focus is on being successful at domestic level, the Manila-born playmaker admits he is hoping that can lead to a senior call.
Smith said: "My focus is here at Quins. That's one game, I've done alright this game but there's still a long way to go and there's a big test on Friday night and hopefully I can carry the performance today and take it into next week along with the team.
"Obviously it's every kid's dream to play for England, that's my goal at the end of the day, but I need to let my performances do the talking here and hopefully get Eddie calling me - hopefully."