The attacking midfielder, 27, 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.
He has scored 10 goals in 20 games for Celtic this season but has drawn a blank in the club's European ties, including the Champions League group games against Barcelona, Manchester City and Borussia Monchengladbach.
Sinclair says he is not concerned that playing in Scotland will hamper his chances of England recognition.
"I wouldn't say there's any barrier, it's just how well you do," said Sinclair, who has also played for Chelsea, Swansea and Manchester City.
"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."
LA Galaxy midfielder and former Liverpool captain Steven Gerrard has been linked with a move to Celtic as he nears the end of his contract, with Celtic boss Brendan Rodgers having worked with the player at Anfield.
"It would be massive if he did come here," said Sinclair. "The fans would take to him.
"He's a world-class player, so I'm sure a lot of players here would learn off him. Once we're in the Champions League and playing the likes of Barcelona and Man City, it attracts more players."
Scott Sinclair believes his performances for Celtic in the Champions League can lead to an England call-up.