The 27 year old attacking midfielder has played for his country at every level up to under-21s.
"When my time's right it will come," said Sinclair. "My ambition is still to play for my country.
"If you're playing Champions League and doing it at that level, I don't see why not."
Sinclair moved to Glasgow from Aston Villa in August, signing a four-year deal.
"I wouldn't say there's any barrier, it's just how well you do," said Sinclair.
"When you're playing every week, you're building confidence and form. My form's back, I'm scoring goals, we're winning games and I can't ask for much more."
Sinclair watched England's 3-0 World Cup qualifying defeat of Scotland on Friday and does not believe there is a significant difference in the quality of the two international squads.
"It was one of those games - it seemed like Scotland played well for the first 30 minutes, and once they conceded, backed off," he said.
"In international football, you've got to take your chances.
"There is quality [in Scottish football]. People underestimate the league and think they can just write it off."