According to Nick Lustig in the Daily Star, the Reds put in a £15 million bid for the 22-year-old last week and are looking good to claim the Swiss international's signature.
The youngster recently expressed his unhappiness at his lack of playing time at Bayern and hinted that he may want out, per 20 Minuten (via the Express' Alex Harris):
We'll see. I'm not going to go through another year like this. If not much changes, then I will have to change something. I am only disappointed because I have played less.
I am young and need to develop myself. I want to play in the big games from the beginning, and not just in the league when everything is already clear.
I want to play at a top club as the Champions League is important to me.
As far as his own criteria goes, Anfield looks like a terrific fit for the former Basel player, who bagged six goals in 17 Bundesliga appearances last season, per WhoScored.com.
Liverpool's second-place Premier League finish last season sees them into the Champions League for the first time since 2009, and Shaqiri would likely be given better opportunities playing for the Reds.
He is also an ideal fit for Rodgers' fast-paced, counter-attacking style that the manager has been developing since he took up the Liverpool post in 2012.
Shaqiri has an impressive burst of pace, terrific balance due to a low centre of gravity and great strength, which would serve him well in the Premier League.
He is naturally left-footed but prefers the right wing, although he can play on either flank, and has an impressive range of passing, especially for such a young player.
He would complement the likes of Daniel Sturridge, Luis Suarez and Raheem Sterling and add to the already blistering pace of Liverpool's attacking unit.
Furthermore, he looks to be terrific value at £15 million. Certainly better value than Rodgers' other midfield target, Adam Lallana, who will reportedly cost the Reds £25 million, per Fox Soccer:
With Champions League football to factor in next season, Liverpool need a stronger squad, and Shaqiri is exactly the kind of player who would constitute a terrific addition to the Liverpool side.
With so many games, star men Sturridge and Suarez are at some point going to be sidelined. Shaqiri's presence would provide a suitable alternative who Rodgers could have confidence in.
Liverpool will want to get the deal done soon as the youngster is about to appear for Switzerland in the World Cup, and if he shines on the world stage his price tag may increase.
He is already in scoring mode, coming off the bench on Tuesday to get Switzerland's second as they beat Peru 2-0 in a warm-up match before the summer's showpiece event in Brazil.
The Swiss will face Ecuador, France and Honduras in in Group E and may well make it through to the knockout rounds, especially if Shaqiri is on song.
Rodgers looks to be recruiting exactly the right kind of players as he prepares his squad for next season, and Shaqiri looks the best of the lot.
He shows all the potential of a future star, and Liverpool would do very well to snap him up soon before he shows the world what he can do in Brazil.