The Switzerland international has two more years remaining on his contract with Liverpool, but could be on his way out of the Merseyside-based club this summer.
Shaqiri has informed the Premier League outfit that he wants to move in search of a new challenge and Anfield officials do not plan to stand in his way if they receive an acceptable offer.
Lazio are said to be leading the chase to sign the 29-year-old, while Spanish sides Sevilla and Villarreal are also interested.
While Italy and Spain are potential destinations, the 29-year-old is also open to the idea of returning to the Bundesliga, according to German broadcaster Sport1.
Shaqiri plied his trade for German champions Bayern Munich for three years between 2012 and 2015 and can imagine returning to the country this summer.
However, there are still no concrete talks over a move for the former Basel winger and it remains to be seen if any club in Bundesliga are interested in signing him.
While Liverpool are said to be valuing Shaqiri at £12m, it is claimed that the 29-year-old could be available for a fee less than £8.5m.
