The Switzerland international, who joined the Bundesliga giants in 2012 after impressing at FC Basel, revealed in an interview with Swiss website 20 Minuten that he is considering his options after a frustrating campaign under Pep Guardiola, in which he was restricted to a mere 10 Bundesliga starts.
"It's clear that I cannot continue like this. If nothing changes, I will have to make some changes myself," Shaqiri said. "I want to play in the important games as well and not just in the Bundesliga. I don't want to go through another year like this.
"I only want to play for a major club. The Champions League is important to me. We will see what happens.
"England would be an option. If I were to leave Bayern, it will be for a foreign club. But it will have to be a club challenging for the title."
Liverpool were already interested in signing the gifted midfielder, who has scored 15 goals in 65 appearances for the 2013 Champions League winners, before his latest revelation. Now, according to the Metro, the Reds will table a £15m offer in a bid to lure the Swiss star to Anfield this summer.
Shaqiri would use up a quarter of Brendan Rodgers' £60m summer transfer budget - but, for the price Liverpool are paying, the Merseyside outfit could potentially secure one of the bargain signings of the summer transfer window.