The 29-year-old endured a frustrating 2020-21 campaign, making just five starts and nine substitute appearances in the Premier League.
With little prospect of earning a regular place in Jurgen Klopp's starting lineup, Shaqiri has acknowledged that he would like to move to Lazio over the coming weeks.
Speaking to Corriere dello Sport, the Switzerland international said: "I told Liverpool board I feel ready for a new challenge. They accepted my decision and will now consider bids to sell me. Liverpool won't stop me this summer.
"I'd love to come back to Italy, and I'd like to play for Lazio."
Shaqiri, who could cost in the region of £12m, spent a short period at Inter Milan in 2015 before signing for Stoke City. body check tags ::