Shaqiri donned a Bayern shirt for the first time during his new side's pre-season friendly against SpVgg Unterhaching.
The Swiss played the full 90 minutes in the 1-0 win and joined fellow new arrivals Tom Starke, Dante and Mitchell Weiser in making his bow for the German giants.
Shaqiri stated that his decision not to play at the Olympics could help him force his way into Jupp Heynckes' reckoning by the start of the season.
"It could be advantageous, but not just for me - for every player who's here [during pre-season]. The internationals not here know when they come back they're going to have to give it 100 per cent," he told Bundesliga.de.
"Of course there is going to be competition for places here. I'm a very versatile player and it's important for players to be flexible in order to increase their chances of playing, but we have to be there for one another and I hope we get off to a good start."
The 20-year-old believes he has acquired a winning mentality during his time with Basel and thinks this will stand him in good stead for the challenges that await him at the Allianz Arena.
"I've come from a club which won a lot of titles and obviously I want to continue that with my new club. The Bundesliga is a stronger league and I'm determined to continue my development, that's why I came to Bayern.
"I think we're on the right track and we've laid the foundations for a good start to the season," he added.