The Italian Serie A side were keen on signing Silva following the expiry of his contract at Manchester City and were confident of landing him.
However, Silva opted to head back to Spain and has put pen to paper to a contract with La Liga side Real Sociedad.
Lazio are now looking at other options and, according to Italian outlet fantacalcio.it, Liverpool's Shaqiri is a potential target.
Shaqiri is a player Lazio have looked at before and they could make a move to take him to the Italian capital this summer.
The Switzerland international has struggled to play on a regular basis under Jurgen Klopp at Anfield and may be tempted by the prospect of moving to Lazio.
A move to Lazio would see Shaqiri play with former Liverpool stars Lucas Leiva and Luis Alberto.
The 28-year-old made just eleven appearances across all competitions for Liverpool over the course of the 2019/20 season.
