Shaqiri has largely been used as a back-up option to Liverpool’s famed front three of Mohamed Salah, Roberto Firmino and Sadio Mane since joining the club from Stoke City in the summer of 2018.
He has made just 45 Premier League appearances in his time at the club.
The former Bayern Munich winger found some of his mojo during this summer’s European Championship, scoring three goals in five appearances as Switzerland reached the quarterfinals.
Shaqiri has a year left on his contract at Anfield but he has expressed an interest in returning to the Italian Serie A, where had a six-month stint with Inter Milan in the second half of the 2014/2015 season.
"Fortunately, football has helped me achieve many of my dreams," Shaqiri told Italian newspaper Corriere dello Sport. "I was lucky enough to play with great teams and to win many titles.
"Who knows, maybe I could get something even with the Swiss national team. My contract [with] Liverpool expires in 2022, in 2018 I signed a four-year deal.
"The important thing at this moment in my career is to be able to play regularly, but that hasn’t always been the case in the last three seasons.
"This is why I told Liverpool that I feel ready for a new challenge. They accepted my wish and will seriously consider the offers that will come. They will not stop me."
"I'm only 29 years old, I have played in some of the best leagues in Europe, and I would like to continue being a part of them," Shaqiri added.
"I’m not yet thinking about the end of my career, it’s a future I imagine far away. We will see what destiny has in store for me.
"I think it’s not just my opinion that football in Italy has developed substantially in recent years. The win at the European Championship is there to prove it, a well-deserved result.
"Just take a look at how many Premier League players have moved to Serie A."
"I have been following Lazio for a long time, they are a top team. In general, due to my characteristics, I like to play more attacking football and Sarri practices it. It would be intriguing."
