The 25-year-old striker has earned six caps for Scotland to date, but he is yet to score for his country.
Griffiths has only been given sporadic opportunities by the Scottish national side, but having been called up to their latest squad, he is hoping to get on the scoresheet.
“I’ve started well but I can’t rest on what I’ve done so far,” he explained. “I need to keep looking forward, playing well, scoring goals and helping the team get back to the top of the league.
“I’ve scored a few times in Europe and that’s been good. You always want to try to score as many goals as you can and play at the top level. I scored a couple in the Champions League and then scored against Fenerbahce in the Europa League so my next aim is to try to score for Scotland on the international stage.”
Scotland take on Poland and Gibraltar in Euro 2016 qualifying over the course of the next week, meaning that Griffiths has arguably never had a better opportunity to get off the mark.
Although Gordon Strachan's side will face a tough test against Poland, their match against Gibraltar should be a guaranteed three points.
Gibraltar have leaked goals throughout their qualifying campaign so far, and if Griffiths takes his club form into the international break, he should have an excellence chance of hitting the back of the net.
The clinical front-man has netted 10 times in 18 matches for Celtic, and his good form has further established him as the Bhoys' main man up front.