The Reds are known to be in the market for forward-thinking additions this summer, with Brendan Rodgers eager to bulk out his squad to cope with Champions League football.
Southampton captain Adam Lallana is said to be the top target, but with the Saints holding out for £30m a deal may be unworkable.
Shaqiri has been mooted as an alternative – or a possible purchase alongside the English playmaker – and now it is understood that the Merseysiders are talking to Bayern about a move.
The Switzerland star – who is at the World Cup – is expected to leave the Allianz Arena before next season officially starts, and has already voiced his displeasure at being an infrequent starter for the Bavarians.
The 22-year-old is seen as a good addition by Rodgers, with his ability to play on either flank or in a central role off of a main striker appealing to the Northern Irishman.
Shaqiri is valued at around £15m.