The 18-year-old was given a taste of first-team action last year by the Hoops manager when an injury crisis meant that he was thrown into a Europa League tie against Rennes at Celtic Park, a game that the Parkhead side won 3-1.
This season, progress has been slower, essentially due to the fact that Lennon was able to strengthen his squad over the summer break.
Signings such as Efe Ambrose, the return to fitness of Emilio Izaguirre and the improved form of Kelvin Wilson, as well as the bedding in of Mikael Lustig who arrived at the club last winter, have all made the road to the first team that little bit tougher.
Yet, with players like Tony Watt, Dylan McGeouch, Patrick and Filip Twardzik making it into the senior pool, Fraser believes that as long as he continues to stick to his task that he will manage to push on and ultimately make his mark.
The defender captained Scotland's Under-19 side to the elite qualification round last week and his sights remain trained on catching Lennon's attention.
"I share a dressing-room every day with the Twardzik lads and I think we have all seen that if the manager thinks you are good enough, then you'll get through," said the teenager.
"I obviously was involved last year in the Europa League game and it was a great experience to be in there.
"But now I am just focused on trying to do the best that I can in training and in games.
Hopefully if the chance comes again this season I will be ready to take it."
Celtic's Champions League campaign, coupled with the fact that there is not the same domestic pressure in the SPL because of the absence of Rangers, means that there is a fair chance the younger players may well be drip-fed into the first team as the season progresses in order to give them some valuable experience.
"That is something that has obviously crossed my mind, but it is just a case of trying to do the best that I can," said Fraser.
"For players such as myself it maybe helps our cause a little bit that Danny McGrain has moved up to the first-team side of things because he knows us well and might be able to put in a good word for us."